Multi-criteria decision-making methods applied in health-insurance underwriting

ABSTRACT

This study attempts to structure methodologically the health insurance underwriting process by applying Multi-criteria Decision-making (MCDM) analysis in health insurance underwriting. This is done by assigning a score to each health insurance applicant which can be used to determine whether he or she is accepted, rejected or accepted with special terms and conditions (such as exclusions, additional waiting periods and/ or surcharge). The introduction of MCDM approaches in health insurance underwriting enables the quantification of the selection criteria, the increased standardization and automation of the process and its alignment through quantitative indicators with the risk tolerance/ risk appetite of the insurer, and there lie the novelties of this research. The proposed methodology can be readily implemented by insurers with added value in the underwriting, risk management and distribution (sales & marketing) functions, as well as in the profitability of the company or the level of premium paid by the insured.

1. Introduction

The scope of an insurance company is to accept and manage risks. Its profit comes from the proper management of the assumed risks so that the benefits paid and the expenses incurred are less than the premium collected (or invested) for the insured population. To secure that, the insurance company needs to establish a process for the proper assessment, selection and pricing of risks. Underwriting is the process employed by insurers to determine whether they will accept a certain risk (globally) or will issue a policy (specifically). Underwriting is based on a set of criteria established by the insurer (for the determination of the decision) and can be subject to local or broader legislation, directives and restrictions. Each underwriting decision aims at balancing (i) the insurer’s appetite to earn premium; (ii) the insurer’s capacity to cover claims; (iii) the shareholder’s (and insurer’s) requirement to make a profit; as well as (iv) the regulator’s demand to stay compliant. There are four basic types of underwriting decisions: (i) issue a policy as preferred in the application (free); (ii) issue a policy as standard (packaged); (iii) issue a policy as substandard (with exclusions, waiting periods, surcharges or limits); and (iv) reject the application.

There are 3 main types of insurance considered: (i) personal: insuring individual lives for life, disability, health, etc.; (ii) property: offering insurance protection for home, motor, commercial property, etc.; and (iii) business operations: providing coverage for general liability, professional liability, etc. For each type of insurance, several factors are employed to assess the risk. For personal insurance the most common factors are: (i) age; (ii) gender; (iii) health condition and medical history; (iv) occupation and occupation history; (v) financial condition; (vi) smoking status (i.e., current and historical); (vii) drinking status (i.e., current and historical); (viii) lifestyle (such as sports, etc.); (ix) size of policy; (x) other insurance coverage in force; and (xi) other indices (such as BMI, etc.). This is evidenced also by the underwriting manuals of insurers (see for example Blue Cross Blue Shield (2012), Aetna (2010), World Insurance (2008), Health Net (2004), American National Life Insurance Company of Texas (2003) and Affordable Educators (2001)).

Health insurance is a type of personal insurance that provides coverage to the insured in case of health-related issues both therapeutic (such as hospitalization) and preventive (such as medical exams). Health insurance thus may refer to inpatient and outpatient healthcare coverage/ policy respectively. The role of the health insurance (or medical) underwriting function is to collect all the necessary documentation and information with regards to the candidate/ applicant risk, assess it against statistical data or prior experience and accept or decline it. If accepted, then a price tag needs to be put on the policy.

Multi-criteria Decision-making (MCDM) or (alternatively called) Multi-criteria Decision Analysis (MCDA) is one of the most well-known and relevant methodological approaches that can be used to decide by assessing a set of criteria. The process involves the elimination of non-qualifying choices, as well as the evaluation of the qualifying ones. The criteria have to be complete and independent (as much as possible). This shows a significant resemblance with the underwriting process, which uses a series of factors to accept or decline insurance to applicants and evaluates individuals that are not immediately rejected.

The question that the present research (research question/ hypothesis) attempts to address is whether Multi-criteria Decision-making methods can be used to assist the health insurance underwriting process provided the relevant factors are known, and even put weight on these factors. If such an application of MCDM methods to the health underwriting process proves to be feasible, then the next question is whether it can be automated to facilitate the underwriting process.

The aim of this research (research aim/ objective) is to show that MCDM approaches can be introduced to the health insurance underwriting process to standardize it, facilitate it, quantify it and even automate it. To achieve this, the factors that are relevant to health insurance are identified and are converted into criteria that reflect the interest/ scope of the underwriter and at the same time fulfill the properties of the MCDM methodology used; i.e., provide a complete set and have the smallest possible correlation. These criteria are then grouped and put in a hierarchical order. Last but not least, a weight is assigned to each of them. The ultimate objective of this study is to finally score/ grade each applicant for health insurance and use this score/ grade to determine his or her rejection, acceptance or acceptance with conditions. The latter means potential exclusions, waiting periods and/ or surcharges. To illustrate how the underwriting process can be facilitated with the use of MCDM approaches we apply two MCDM methods; the weighting sum method (WSM) and PROMETHEE. The presentation of each MCDM method is complemented with a numerical example which pertains to the application of WSM and PROMETHEE in the actual insured population of an insurance company.

The application of MCDM methods in health insurance underwriting is important to investigate because the quantification, standardization and automation of the health insurance underwriting process – which is highly qualitative, not fully standardized and to some extent manual – is key for the insurer as: (i) it permits the alignment of the accepted risks (applicants) with its risk tolerance/ appetite; (ii) it can reduce the cost of the underwriting process; (iii) it can render the underwriting process leaner and seamless; and (iv) it allows for increased transparency and simplicity for all stakeholders (applicants/ candidates, distributors and underwriters – even regulators). The existing literature however has not covered the employment of MCDM methods in health insurance underwriting. As a matter of fact, it has not addressed the use of MCDM methods in insurance underwriting at all, as becomes apparent in the literature review section that follows. There have been some applications of MCDM approaches in finance, healthcare and (health) insurance – all of which are presented in the literature review section – but with a different perspective from (this of) underwriting.

Τhe contribution of the present study in the field lies precisely in the use of MCDM methods in health insurance underwriting to quantify, standardize and automate the underwriting process. As this has not been exploited in the past, to the best of the authors’ knowledge and as evidenced by the existing literature, it further advances the new knowledge in the field, and offers new ways of understanding the health insurance underwriting function. The recommended approaches can be of added value to the insurers that wish to employ scientific methods to improve their underwriting process and make it more efficient and transparent for all interested parties (as per item (iv) above).

2. Literature review

A bibliographical search showed that no literature has been produced in that direction. It is a question mark why, as Multi-criteria Decision-making seems to have been utilized already in finance. To demonstrate this gap the representative available literature of (i) insurance underwriting methods; (ii) applications of MCDM in finance; (iii) applications of MCDM in healthcare; (iv) applications of MCDM in (health) insurance; and (v) MCDM methods is presented. This grid of topics was selected as it covers the bibliographical spectrum in the fields of insurance underwriting (not health insurance underwriting only) and MCDM; it reveals that the application of MCDM in (health) insurance underwriting has not been captured.

The literature review search was conducted with the use of a series of keyword combinations in Google and Google Scholar; these are: multi-criteria decision analysis and insurance, multi-criteria decision-making and insurance, multi-criteria decision analysis in finance, multi-criteria decision-making in finance, multi-criteria decision analysis in healthcare, multi-criteria decision-making in healthcare, and insurance underwriting method(s). The relevant articles were kept and studied under the prism of the present study; namely, their contribution either to insurance underwriting or to the use of MCDM in finance, insurance and healthcare. The details appear in Appendix A.1, in Table 13 and in the PRISMA diagram of Figure 3 of the same Appendix A.1.

Table 13.

Keyword combination searches at google and google scholar.

Combination	Keyword terms
1	multi-criteria decision analysis and insurance
2	multi-criteria decision-making and insurance
3	multi-criteria decision analysis in finance
4	multi-criteria decision-making in finance
5	multi-criteria decision analysis in healthcare
6	multi-criteria decision-making in healthcare
7	insurance underwriting method(s)

Created by the authors

The literature review displays the available research on a series of relevant topics. These are insurance underwriting methods (in life insurance, fire public liability insurance, and motor insurance); the application of MCDM in finance; the application of MCDM in healthcare; the application of MCDM in (health and other types of) insurance; and MCDM methods globally. The literature review is depicted in a concise form in Table 1 that follows. The detailed literature review is presented in Appendix A.2

Table 1.

Literature review.

Author & Year	Topic
	Insurance underwriting methods – Life insurance
Society of Actuaries (2018)	Life insurance underwriting methods employed or envisaged (for the future) by insurers fall in three categories: traditional, accelerated and simplified underwriting. These methods are further distinguished in triage, accelerated underwriting, predictive analytics, artificial intelligence (AI)/ cognitive computing, algorithmic underwriting, simplified issue (SI), rules engines, electronic data, tele-underwriting and other tools/ data.
	Insurance underwriting methods – Fire public liability insurance
Han (2011)	Fire public liability insurance in assembly occupancies risk assessment and underwriting auditing with a focus on life safety can be standardized with a scoring scheme that resembles the one used in MCDM.
	Insurance underwriting methods – Motor insurance
Kitchens (2009)	Artificial neural networks are recommended over linear and logistic models
	MCDM in finance
Spronk et al. (2016)	Focus on the multi-dimensional character of financial decisions and the employment of MCDA approaches to back them as well as on the illustration of their advantages.
Doumpos and Zopounidis (2014)	Present the contribution of MCDA in addressing the various topics of financial decision-making, as well as the principles of MCDA and its applications in specific areas.
Zopounidis and Doumpos (2002)	Highlight the importance of Multi-criteria Decision aid (MCDA) in financial decision-making and its contribution to finance, emphasizing real-world applications.
Steuer and Na (2003)	Provide a categorized bibliographic study on multiple criteria decision-making (MCDM) combined with finance.
	MCDM in healthcare – literature review/ bibliometric analysis
Frazão et al. (2018); Adunlin et al. (2015); Marsh et al. (2014); Diaby et al. (2013); and Liberatore and Nydick (2008)	Perform a literature review/ bibliometric analysis and categorize the articles available in the area of MCDA in healthcare (decision-making).
	MCDM in healthcare – books/ collective issues
Marsh et al. (2017),	A collection of articles attempt to present and tackle the challenges (technical and political) that pertain to the application of MCDA in healthcare decision-making.
González et al. (2018)	Have edited an assortment of articles in the same directions with contributors from Spain.
	MCDM in healthcare – individual papers
Hansen and Devlin (2021),	Elaborate on the use of MCDA in healthcare decision-making as it assists in the evaluation of alternatives.
Marsh et al. (2016)	Report on the good practice guidance on the use of MCDA in healthcare decisions.
Thokala et al. (2016)	Present (in two reports) the emerging good practices of MCDA in healthcare decision-making.
	MCDM in healthcare – healthcare economics
Jit (2018); and Norman et al. (2018)	Address the employment of MCDA in healthcare economics, with the extension of economic evaluation methods such as cost-effectiveness analysis and cost-benefit analysis to reach healthcare investment decisions or designing/ enlarging public health insurance schemes.
	MCDM in healthcare – country specific
Pereira et al. (2020)	Employ MCDA to rank nine of the European health systems with Beveridgian financing to identify the weaknesses of the Portuguese National Health Service and recognize potential best practices.
Öztürk et al. (2020	Use MCDA – and in particular MCDA4HTA – in HTA (health technology assessment) decision-making and apply it in the case of Turkey.
Defechereux et al. (2012)	Look at the MCDA as a means for healthcare priority setting in Norway.
	MCDM in (health) insurance – optimal selection of health plan
Pattnaik et al. (2021)	Propose an MCDM model (fuzzy MCDM combined with the technique for order preference by similarity to ideal solution – TOPSIS) to facilitate the (online) purchase of life insurance coverage in India.
Guo (2017)	Uses MCDA to address health insurance for foreigners in the Czech Republic.
	MCDM in (health) insurance – motor insurance
Esfandabadi et al. (2020)	Employ MCDA approaches (a two-phase process based on fuzzy Delphi method – FDM and fuzzy analytic hierarchy process – FAHP) to identify and prioritize important risk factors relevant to the personal and behavioral attributes of the drivers on top of the vehicle characteristics.
Heras et al. (2015)	Realize the multi-objective nature of bonus-malus systems insurance as it attempts to meet three objectives; fairness, toughness and (dis)equilibrium.
	MCDM in (health) insurance – company corporate issues
Gharizadeh Beiragh et al. (2020)	Assess the sustainability performance of insurance companies with MCDM.
Rubio-Misas and Gómez (2015)	Use MCDM (cross-frontier methodology based on data envelopment analysis – DEA) to assess the relative efficiency of stock (owned by stockholders) and mutual insurance companies (owned by policyholders).
	MCDM in (health) insurance – insurance coverage
Shahabi et al. (2021)	Use MCDM (a qualitative study complemented with an analytical hierarchy process (AHP)) to draft recommendations that will improve the insurance coverage for physiotherapy services.
	MCDM in (health) insurance – health insurance underwriting
Bly (2004)	Presents international medical underwriting approaches, along with their impact on profitability and compares them with the approach followed in the USA.
	MCDM methods
Velasquez and Hester (2013)	Describe the methods that have been developed over the years, examine their advantages and disadvantages and explain how their applications relate to strengths and weaknesses.
Mourmouris (2006)	Paves a good path for setting the methodology, the criteria, the weights and scoring and finally applying MCDM for the evaluation.
Batty and Kroll (2009)	Realize (through a survey) that there seems to be room and need for automated life insurance underwriting

Created by the authors

In summary, we realize that the use of MCDM in insurance focuses on the (optimal) selection of an insurance plan; the identification and prioritization of important risk factors relevant to the personal and behavioral attributes of the drivers; the valuation of the objectives of the bonus-malus systems; the assessment of the sustainability of the performance of insurance companies; the assessment of the relative efficiency of stock (owned by stockholders) and mutual insurance companies (owned by policyholders); and the insurance coverage for physiotherapy services. Furthermore, the literature on medical underwriting unveils the approaches employed, which are the extensive use of riders to limit coverage for specific conditions; the reliance upon a medical professional judgment for rating purposes; and the application of life insurance underwriting guidelines or US medical underwriting guidelines. Consequently, when it comes to health insurance underwriting, we realize that MCDM is not among the established approaches.

The above indicates that the contribution of our paper is twofold, as on one hand it introduces MCDM in health insurance underwriting and on the other hand it sets the ground for automation in health insurance underwriting.

3. Problem description

Before addressing the problem that this study investigates, we offer a brief description of the health insurance (underwriting) problem.

3.1. Health insurance (underwriting) problem

Health insurers need to address a very specific problem when running their operations. Namely, they have to decide whether to accept or not an individual and if yes with what terms and at what price. Health insurance or medical underwriting is the process employed by a (private) insurer to assess/ determine whether health coverage will be offered to an applicant/ candidate or not, and if so with what potential exclusions, deductible amounts or limits and at what rate/ premium/ price (HealthCare.gov (2021); healthinsurance.org (2021)). Consequently, the health insurance underwriting process aims at reaching a decision first on the acceptance of the applicant, and – conditional on his or her acceptance – on the terms and the premium. It is based (among others) on the health/ medical history, the age, the type of employment, the geographical region of domiciliation and the lifestyle/ behavioral preferences – if relevant (e.g., smoking status, etc.) – of the applicant (Blue Shield of California (2006); Xu (2020)).

There are two types of health insurance underwriting; moratorium underwriting and full medical underwriting. The former asks only a small number of questions and automatically excludes all pre-existing medical conditions (at least for several years) even if they become known/ disclosed to the insurer at the time the insured files for a claim. The latter requires full disclosure of the health/ medical history at the time of the application and the applicant has to answer a detailed medical questionnaire. The former has the advantage of offering a health insurance policy faster – in case of acceptance, but has the disadvantage of potentially not reimbursing a claim if relevant to a pre-existing condition – leading to uncertainty. The latter has the advantage of providing explicit knowledge of what is and what is not covered from the time of policy issuance – upon acceptance, hence offering certainty, but has the disadvantage of a potentially longer application examination process (Health 401k (2011); Freedom Health Insurance (2021)). This paper focuses primarily on full medical underwriting.

Medical underwriting employs a series of guidelines, along with professional judgment to reach the aforementioned decision(s). The collection of data from health insurers along with the digitization of the process can facilitate the modernization of medical underwriting. Three dimensions need to be pursued (Deloitte (2021); Bly (2004)) to achieve that:

1. Underwriting decisions need to be well informed before being taken and not to be evaluated after the fact has occurred.

2. Underwriting needs to be based more on science – which allows for more rigorous rules and automation, even though professional judgment (which is somehow more of an art) will always be there.

3. Underwriting has to adapt to the changing nature of risk and if possible predict this evolution, to ensure relevance and competitiveness.

Is there a way to address these dimensions when pursuing medical/ health insurance underwriting? This manuscript offers MCDM as a potential solution to the health insurance/ medical underwriting problem.

3.2. MCDM as a solution to the health insurance (underwriting) problem

The solution attempted through this research is to transfer the underwriting decision process into an MCDM environment and then apply the MCDM methodology to reach a decision on the rejection, acceptance or acceptance with special conditions of a candidate/ applicant and hence the issuance (or not) of the respective health insurance policy.

The evaluation process (as explained above in section 3.1) traditionally starts with the collection of data via the insurance application. The latter can be in a paper format or paperless-digital (online completion or telephonic interview). If needed – and depending on the answers given on the medical questionnaire with regards to the demographic particulars and health condition of the applicant – medical exams may be asked so as to gain additional intelligence and better support the acceptance (or not) of the candidate. The factors considered in the evaluation of the application cover almost the full spectrum of aspects of the life of the person to be insured; however they are not explicitly grouped (some implicit categorization is in place), they are not ordered in terms of importance for the decision, and they are not weighted (at least to the best of the knowledge of the authors). Hence the decision-making process is mainly qualitative.

On the other hand, the MCDM approach utilizes the appropriate criteria to facilitate the decision-making process by grouping the relevant criteria, ordering them hierarchically and assigning a weight to them. Although such grouping, ordering and weighting could be highly subjective it globally provides a numerical output that can be used for comparing the available options. Such a score is not interpreted in absolute terms but rather in relative terms, to rank the options under evaluation and choose the ones that score above a certain level. The latter is also subjective; however, it provides a more quantitative framework. The subjectivity can be contained by using a consensus of the experts’ opinions and by aligning the scores with the targets of the company – in particular its risk tolerance/ risk appetite.

We use the MCDM methodology to quantify (as much as we can) the underwriting process and equip it in such a way with a tool that can enable it to reach the acceptance (or rejection) decision in an easier and justified manner, thus enabling the automation of the process. To confirm the validity of our proposal, we maintain the characteristics of the traditional approach. We attempt to calibrate such a scoring approach to better match the decisions taken through the current underwriting process. To secure the reliability of the model we test its sensitivity – again versus the decisions taken with the current process – by perturbing the weights assigned to the criteria employed.

Insurance underwriters are (still) urged to bring science into the insurance underwriting art (Deloitte (2021)). The present paper helps address all these three dimensions as it quantifies a rather qualitative process enabling the evaluation of underwriting decisions in advance (dimension 1), it introduces MCDM as a scientific approach (dimension 2) and uses the accumulated experience to recalibrate the model(s) so as to follow the evolution of the associated risks (dimension 3).

In our study, we proceed with the assumption that full medical underwriting is possible, i.e., that full disclosure of the health/ medical history at the time of the application is required and a detailed medical questionnaire has to be filled in by the applicant. We do realize though that depending on the country/ region this may not be possible. Examples are the gender-neutral pricing in the insurance industry in the European Union (EU) that entered into force in 2012 (European Commission (2012)) and the Patient Protection and Affordable Care Act (PPACA) in the United States, which took effect in 2014 (govinfo.gov (2010); Claxton et al. (2016)). The former has been depicted in our study, as our numerical example applies to an insurance company in an EU country (Greece); thus male-female applicants are not given different scores, even though gender is a differentiating factor in health insurance (experience and consequently rating). The model introduced in the paper can be aligned with the legal/ regulatory requirements applicable to the country of interest by removing the criteria whose use may be restricted (in that country).

4. The MCDM approach

Multi-criteria Decision-making (MCDM) is a term used to describe (a series/ set of methods employed in) decision-making which use(s) multiple criteria/ objectives/ standards/ factors that lead to the ranking/ prioritization of the different alternatives/ choices (which can be individuals). In such a way, the decision-making process is/ becomes structured and at the same time facilitated, as the selection of the different alternatives is based on their rank. MCDM is therefore an umbrella term and does not refer to a single method. MCDM methods can be applied to a wide array of cases such as the selection of projects or investments, the prioritization of local or central government spending, the prioritization of patients for access to healthcare, short-listing applicants and many more.

MCDM is considered a discipline of operations research and employs economics, psychology and mathematics to structure and solve decision problems. The MCDM methods assign a specific weighting to the criteria and the (potential) trade-offs between them to formalize the decision-making process. In this way, MCDM aims at minimizing the effect of the potential bias stemming from intuitive or group-based decision-making approaches. The introduction of specific, explicit weights to the criteria leads to more rigorous, well-informed, transparent and consistent decision-making processes, that when applied produce outcomes that are independent of the individual(s) executing them.

The MCDM process can be broken into three main stages/ parts/ phases, which are the identification of the problem and its structuring, the building of the model and its subsequent use, and finally the development of action plans (Belton & Stewart, 2002). This is presented In Figure 1 that follows. The details of the stages and the stakeholders of the process are presented in Appendix B.1.

Figure 1.

The MCDM process.

Source: Created by the authors with input from Belton and Stewart (2002)

There is one additional distinction of MCDM problems with regards to the number of alternatives (or individuals) considered; namely one-off and repeated problems. The former involves the application of MCDM methods to rank the alternatives (or individuals) under evaluation to reach a decision once. The latter entails to the implementation of MCDM methods to rank alternatives (or individuals) that are changing over time.

In summary, MCDM comprises four constituents: the alternatives/ choices (or individuals) that are (to be) ranked (or chosen from); the criteria/ objectives/ standards/ factors that are used to evaluate and compare the alternatives; the weights that indicate the relative importance of criteria; and the stakeholders (primarily the decision-makers) whose interests need to be considered.

Following the aforementioned discussion, we realize that the factors/ criteria typically used in the underwriting process are the ones mentioned in the introduction of the paper, i.e., (i) age; (ii) gender; (iii) health condition and medical history; (iv) occupation and occupation history; (v) financial condition; (vi) smoking status (i.e., current and historical); (vii) drinking status (i.e., current and historical); (viii) lifestyle (such as sports, etc.); (ix) size of policy; (x) other insurance in force; (xi) other indices (such as BMI, etc.). We split them into four main categories: demographic; lifestyle; insurance; and financial. In each category, we choose the appropriate criteria to define the elimination and/ or evaluation criteria of the MCDM methodology that we (will) apply.

• Demographic criteria

  • Age: the years from birth
  • Gender: male or female
  • Occupation history: the history of the professions
  • BMI (Body Mass Index = Weight/ Height² → may be replaced by Weight and Height combined/ together)
  • Residence: The place of domiciliation
• Lifestyle criteria

  • Smoking status: the current and historical smoking habit, including the number of cigarettes
  • Drinking status: the current and historical (alcohol) drinking habit, including the number of glasses
  • Sports: athletic activities
  • Motorcycle riding: the use of motorcycles for transportation
  • Military service: time spent serving in the armed forces, especially as a compulsory period for young people in some countries
• Insurance criteria

  • Health history: an assessment of all factors affecting an individual’s health status, including the health of his or her ancestors
  • Medical condition: a current or recent disease, illness or injury
  • Medication: any substance used in treating a disease or relieving pain
  • Size of policy: the maximum amount covered including internal limits as well as deductible and coinsurance
  • Other policies: additional active individual or group health policies
• Financial criteria

  • Income: the flow of cash or cash-equivalents received from work (wage or salary), capital (interest or profit), or land (rent).

To complement the presentation of the constituents of MCDM, we see that the individuals (alternatives) to be ranked are the applicants for health insurance. The weights that indicate the relative importance of the criteria are presented in Section 5. The decision-makers are the underwriters and (through them) the insurers; other stakeholders include the applicants, the intermediaries/ distributors, the healthcare providers, the risk management team, the actuarial function, the claims department, the marketing department, the product development division and the consumer associations, as well as the regulators. The application of MCDM in health insurance underwriting constitutes a repeated MCDM problem.

4.1. Elimination criteria

Mimicking the MCDM approach we identify elimination criteria in the case of health insurance underwriting. The elimination criteria are used for rejecting candidates that do not qualify for a health insurance policy even before filling in an insurance application. They are taken from all the aforementioned types of criteria (demographic, lifestyle, insurance and financial) and are extensively presented in Appendix B.2. The remaining candidates are evaluated, using the evaluation criteria as per the following subsection. Even if an individual passes the elimination criteria, he or she could still be rejected after the evaluation takes place.

4.2. Evaluation criteria

The remaining candidates, i.e., the candidates that have not been rejected, are evaluated, using the evaluation criteria. The evaluation criteria need to fulfill two basic principles:

1/ Completeness, i.e., that the full set of the criteria used to cover all dimensions of interest to the underwriter and provide all the necessary information that needs to be collected is considered.

2/ Independence, i.e., the criteria are not related to each other. We will assume that this is the case; however one can easily understand that the occupation or the age of the insured or the smoking status could lead to medical conditions that affect the acceptance of the candidate.

The evaluation criteria are derived from all the previously reported types of criteria (demographic, lifestyle, insurance and financial) and are rigorously described in Appendix B.3.

4.3. Completeness and Independence

The aforementioned criteria are believed to comprise a complete set as they cover the full range of items/ parameters that are crucial for health insurance underwriting. This is derived on one hand from the generally accepted market practices followed by insurers (see for example Blue Cross Blue Shield (2012), Aetna (2010), World Insurance (2008), Health Net (2004), American National Life Insurance Company of Texas (2003) and Affordable Educators (2001)) and on the other hand because the health of an individual (being the subject of insurance) is affected and determined by them and is dependent on them.

These criteria are independent as they cover different aspects of the health of the individual. One could claim that the medical condition or the medication is affected by the health history of the candidate. However, from the angle of the insurer, these items need to be declared independently, as medication could reveal hidden or unknown diseases. In addition, the current medical condition could be improved versus the health history, provided past health problems have been appropriately treated. Overlaps could exist in practice. However, at the time of the insurance application, these items are complementing the profile of the applicant.

4.4. Generalizability, applicability and alignment with market practices

These evaluation criteria have been collected from insurance companies that perform full medical underwriting. One of them is the insurance company that provided the data, which prefers not to be mentioned. Other representative insurers that use them are referred to in the manuscript (Blue Cross Blue Shield (2012), Aetna (2010), World Insurance (2008), Health Net (2004), American National Life Insurance Company of Texas (2003) and Affordable Educators (2001)) with a summary table (Table 6) presented in (the relevant) section 5 below. These criteria have been developed by insurers and external advisors, with the contribution of actuarial teams, clinical consultants/ physicians, combining claims experience and clinical data as well as expert judgment.

Table 6.

Example of criteria employed by insurers.

Source Criteria	Blue Cross Blue Shield (2012)	Aetna (2010)	World Insurance (2008)	Health Net (2004)	American National Life Insurance Company of Texas (2003)	Affordable Educators (2001)
Demographic
Age	X – Elimination or combined with certain diseases	X – Elimination or combined with certain diseases	X – Elimination or combined with certain diseases	X – Elimination or combined with certain diseases	X – Elimination or combined with certain diseases	X
Gender	X	X	X	X	X	X
Occupation (history)	X – Elimination		X – Elimination	X – Elimination	X – Elimination	X
BMI (height & weight)	X – Surcharge	X – Surcharge & related to diseases	X – Surcharge	X – Surcharge	X – Surcharge	X
Residence (Residency)	X – Residents only	X – Residents only	X	X – Residents only	X – Residents only	X
Lifestyle
Smoking status (use of tobacco)	X – Lower rate if no-tobacco use or combined with certain diseases	X – Lower rate if no-tobacco use or combined with certain diseases	X – Lower rate if no-tobacco use or combined with certain diseases	X – Lower rate if no-tobacco use or combined with certain diseases	X – Lower rate if no-tobacco use or combined with certain diseases	X
Drinking status (use of alcohol)	X – Related to alcoholism/ alcohol abuse/ certain diseases	X – Related to alcoholism/ alcohol abuse – dependency/ certain diseases	X – Related to alcoholism/ alcohol abuse/ certain diseases	X – Related to alcoholism/ alcohol abuse/ certain diseases	X – Related to alcoholism/ alcohol abuse/ certain diseases	X
Sports/ Hobbies	X – Professional		X – Professional or hazardous		X – Hazardous	X
Motorcycle riding			X – Racing
Military service					X	X
Insurance
Health history	X	X	X	X	X	X
Medical condition	X	X	X	X	X	X
Medication	X	X	X	X	X	X
Size of policy				X		X
Other policies						X
Financial
Income					X	X

Created by the authors from insurance company online underwriting manuals

Consequently:

• These criteria are general(izable).

• They are globally used by health insurance companies.

• These criteria are public via the paper and/ or online manuals and/ or applications and/ or tele-underwriting scripts of the insurers.

• The data are collected as a prerequisite for deciding on acceptance, rejection or acceptance with special terms and conditions and/ or surcharge and/ or deductible and/ or waiting periods.

  • They cannot be released to other parties – due to data protection legislation, unless the applicants provide their consent, as is the case when medical examinations are needed to reach a decision.

• The proposed model can be adapted to countries that apply limitations; the criteria that cannot be used will have to be removed from the model. The relevant weights will have to be recalculated.

The novelty introduced through this paper is that it employs MCDM to quantify the criteria used in the underwriting process. This facilitates the quantification of the (highly) qualitative underwriting process. Such an approach has not been found in the available research, although it seems to be in line with the contemporary market trends.

As a matter of fact, indicative of the current industry heuristics is also the approach followed by professional consultants, like Milliman, that attempt to develop their own medical underwriting guidelines (Milliman (2021). The approach assigns debit points to the individuals that allow underwriters to place relativities that reflect the health status of the applicants and/ or insured, via a relative morbidity score. Assisted by this tool, the underwriting process leads to a decision, such as acceptance, rejection, acceptance with exclusions or acceptance with a premium surcharge (Milliman, 2021). This tool – although not fully disclosed, provides evidence that our route can be applied also in practice allowing for the quantification and automation of the underwriting process.

4.5. An overview of the MCDM methods

MCDM (Multi-criteria Decision-making) is an umbrella term used to describe a set of methods that are used to structure the decision-making process. When multiple criteria (in contrast to a single criterion) need to be combined then the method employed falls under the umbrella of MCDM. Consequently, the use of more than one criterion to reach a decision means that a Multi-criteria Decision-making (MCDM) method is employed. The MCDM methods can be separated into cost-benefit analysis, elementary methods, multi-attribute utility theory (MAUT) or multi-attribute value theory (MAVT) methods and outranking methods. Their particulars are presented in Appendix B.4

Following the attributes of the different methods, we realize that the multi-attribute utility/ value theory and the outranking methods are the most suitable to facilitate the health insurance/ medical underwriting process as it entails the synthesis of multiple criteria to reach a decision. They are chosen over cost-benefit analysis as they do not rely solely on the assessment of benefits versus cost. They are more suitable than the elementary methods because they refer to more than just a small number of criteria and alternatives. They are more appropriate than group decision-making as there is a single decision-maker, the underwriter (which could be the underwriting team or the insurer).

We selected the weighting sum method (WSM) from the multi-attribute value theory methods because it is simple to understand and communicate as it is based on the addition of the scores of each criterion multiplied by the corresponding weights. At the same time though it can reflect the trade-offs among the different criteria. It can capture the intuition of the decision-makers, the calculation is easy to comprehend, and does not rely on complex computer programming. This makes it suitable for assisting the medical underwriting process which needs to incorporate the expertise of the underwriter and at the same time balance the different criteria to produce one single outcome, i.e., rejection, acceptance or acceptance with special terms and conditions and/ or waiting periods and/ or surcharge (Belton & Stewart, 2002; Fülöp, 2005). Its limitations and the ways to overcome them are mentioned in section 6.7 that follows.

We chose PROMETHEE from the outranking methods because it is also easy to use and does not require that the criteria are proportionate. It offers transparency and takes into account uncertainty and provides a complete ranking of the alternatives. Furthermore, it has increased sophistication versus the ELECTRE methods as it embeds preference modeling. These attributes render it a suitable method for the medical underwriting process as it can offer a ranking of applicants (based on the historical experience of the insurer, without necessarily assuming that the criteria are proportionate) and group them into three clusters; applicants rejected, accepted or accepted with special terms and conditions and/ or waiting periods and/ or surcharge (Belton & Stewart, 2002; Fülöp, 2005). Its limitations and the ways to overcome them are mentioned in section 6.7 that follows.

The particulars of the weights and the methods used are presented in sections 5 and 6 respectively that follow.

4.6. Contribution of the proposed approach to health insurance underwriting

The discussion in subsection 4.5 unveils the contribution of our approach to health insurance/ medical underwriting; namely the employment of MCDM methods in the health insurance underwriting process to synthesize all the available information and selection criteria into one single numerical value which can assist underwriters/ insurers to decide on the rejection, acceptance, or acceptance with special terms and conditions and/ or waiting periods and/ or premium surcharge of the individual that applies for health coverage. The selection of MCDM methods (and in particular multi-attribute utility/ value theory and the outranking methods) is deemed appropriate over other methods as they are the approaches that combine multiple criteria to facilitate the decision-making process and health insurance underwriting does indeed rely on multiple criteria. With the contribution of the recommended MCDM methods, the risk selection process undertaken by the health insurance underwriting function becomes more transparent, standard, homogeneous and quantitative and the same time less subjective. Furthermore, as will become evident after the presentation of the approaches, the recommended models can be calibrated to match the risk profiles that the insurer wishes to accept (in line with its risk appetite/ tolerance). Consequently, the contribution of the proposed methodology expands in that it becomes a valuable tool in the hands of the management teams as they can implement strategies that will give them competitive advantage by attracting the desired risk profiles that fall within the prescribed risk tolerance/ risk appetite level.

4.7. Association with the healthcare system

Health insurance organizations constitute an integral part of a healthcare system as per the World Health Organization (WHO) definition (World Health Organization, 2007). The WHO distinguishes 6 blocks in a healthcare system: service delivery; health workforce; information; medical products, vaccines & technologies; sustainable financing and social protection; and leadership/ governance. Furthermore, the WHO sets 4 overall goals/ outcomes for a healthcare system: improved health; responsiveness; social and financial risk protection; and improved efficiency. Health insurance is associated mainly with the financing block of a healthcare system (World Health Organization, 2007). However, health insurance – besides the controversies surrounding the risk selection process – is linked also to social protection as it assists in establishing financing fairness – even for the lower-income population (World Health Organization, ‎2000 & 2007). This is because, in the absence of a health insurance policy, individuals have to make out-of-pocket payments, which can lead to immense expenses and consequently impoverishment. Health insurance is considered a form of pre-payment within a healthcare system/ universe that pools risks across population groups. In this way, it reduces reliance on out-of-pocket payments.

Although it is not within the scope of this paper to draft policymaking recommendations, we note that the success of a healthcare system depends heavily on the well-orchestrated coexistence of private with (a probably mandatory) public health insurance – also highlighted by the WHO (World Health Organization, ‎2000). This is since whenever both exist, coordination of benefits can provide increased coverage with more affordable premiums even to the lower-income individuals. The latter can be achieved (for example) with the introduction of deductible amounts or coinsurance percentages.

The main contribution of health insurance within a healthcare system is that it replaces an uncertain and potentially very high cost/ loss – such as the out-of-pocket payment of a medical expense – that is known ex-post, with a certain and materially lower cost/ loss – such as the premium – that is known ex-ante. From this perspective, the disbursement of a health insurance premium is preferred over an out-of-pocket payment, as it is more predictable and to a certain extent under the control of the individual (World Health Organization, ‎2000). The affordability and fairness of commercial premiums – provided coverage is offered – in line with the risks, or the exclusion from the insurance of people that need it most, are points of debate among the stakeholders (insured, insurers, regulators, etc.). Besides that, health insurance contributes in several other ways and in more blocks within a healthcare system such as offering protection from catastrophic health events, which improves individual, family and community wellbeing; encouraging, urging or supporting people to remain healthy; improving access to healthcare; facilitating access to supplementary medical services for no or low fees; assisting in the containment of healthcare delivery costs through negotiations with healthcare providers; and enhancing and ensuring the quality of the services provided (see also American Hospital Association, 2019 or Dey & Bach, 2019). The last four, besides the sustainable financing and social protection block, are associated with the service delivery as well as with the medical products, vaccine and technologies blocks. Consequently, health insurance contributes to achieving health improvement, social and financial risk protection, as well as improved efficiency, which are three of the four goals of a healthcare system.

Health insurance is a risk-pooling mechanism where healthy individuals subsidize those who become or are sick. In this respect, it needs to balance two opposing forces; the offering of coverage and the affordability/ fairness of premium. Consequently, the risk selection process, i.e., the underwriting process/ function is probably the most important one. The introduction of the recommended MCDM approaches within the underwriting function helps elevate the contribution of health insurance within a healthcare system in more than one way. More specifically:

• The health insurance underwriting function becomes more transparent, standard, homogeneous and quantitative and less subjective (as highlighted in section 4.6 above).

  • This further promotes fairness in the selection process.
  • It limits anti-selection (or adverse selection), which contains the chances of unexpectedly increasing costs.
  • It can attract more applicants as they will know what to expect as the process will not be a “black box” to them.
  • It, therefore, facilitates access to healthcare which is important for health maintenance/ preservation.
• Health insurers can address market segments that they have excluded in the past.

  • This can include even individuals with diseases, provided their overall score indicates that they can be accepted.
• The health insurance product development and management process is facilitated as insurers can offer products that better cover the needs of the insured.

  • This can include products that cover diseases or individuals that would have been excluded, which enhances fairness in the product offering process.
  • Riders that impose exclusions may be limited, with enhanced product offerings.
• It is anticipated that the health of (even) applicants will improve as they may pay more attention to the lifestyle/ behavioral criteria when they realize the importance they have in the selection process.

  • An example is smoking, which is linked with cardiovascular diseases, cancer, etc.
• It promotes prevention, well-being and healthy living, as applicants can readily assess the importance of demographic or insurance criteria.

  • Examples are the BMI or the health history which can be influenced by nutritional habits, exercise, etc.
• It increases the negotiating power of health insurers towards healthcare providers – on behalf of their insured, as they will have a better knowledge of the selected risks.

  • This can contain the healthcare delivery costs, which is beneficial for the loss/ claims ratio and thus for the level of premiums.
• Pricing can be fairer and more accurate and thus more affordable and competitive and at the same time adequate assuming that:

  • The insurers will return to the insured part or all of the excess profit that will result from the increased accuracy in the selection process and the subsequent benefits as described above, which will lead to a lower initial premium.
  • Re-pricing at the anniversary will not be necessary (except potentially for age), as the underwriting process led to the successful selection of the desired risks.

These benefits, which can be achieved from the introduction of the MCDM approaches in health insurance underwriting, are associated with the financing and social protection, as well as the service delivery blocks. They are also relevant to three of the goals of a healthcare system; namely health improvement, social and financial risk protection, as well as improved efficiency. Having said that, we need to mention that they do not constitute a panacea; there will still be individuals that will not be accepted or will receive a higher premium than they anticipate or afford. However, the transparency, standardization and homogeneity of the underwriting process will contribute to fairness, which is among the key quests of a healthcare system (World Health Organization, ‎2000).

5. Weighting and scoring of the underwriting criteria

After the criteria have been established, they are put in hierarchical ordering and weights are assigned to them. To achieve this we will try to utilize as much as possible the underwriting expertise available, at least for the relative importance of the different criteria. For the hierarchical ordering the following scales are applied (Table 2):

Table 2.

Hierarchical ordering scales.

Criteria	Scales
Demographic	1–3
Lifestyle	1–3
Insurance	1–5
Financial	1–3

Created by the authors for the assessment of the importance of the criteria

All scales have the highest score being the best. Scales are taken for the positive integers in the range indicated and no intervals or smaller refinement is considered. Such scaling allows the assignement of a “value” to each criterion to reflect its importance as would be perceived by the underwriting process. This approach leads to the following Table 3 for the aforementioned criteria.

Table 3.

Importance of criteria per group.

Criteria	Importance	Comment
Demographic
Age	3	High importance, as according to age certain medical conditions or behavior (proneness to accidents) could be anticipated
Gender	1	Used primarily for the evaluation of medical history – other use considered discriminatory
Occupation history	2	Medium importance, as occupation history could lead to the development of certain illnesses or could reveal potential accidents
BMI	3	High importance as BMI is an indicator of potential future diseases
Residence	1	Used mainly for the estimation of the frequency of occurrence of diseases
Lifestyle
Smoking status	3	High importance as smoking even as a prior habit is highly associated with the development of a series of diseases
Drinking status	3	High importance for reasons similar to smoking
Sports	2	Medium importance as certain sports, especially motorsports could lead to accidents
Motorcycle riding	2	Same as above, even if a motorcycle is used as a routine transportation means
Military service	1	Low importance as service or exemption could be fairly typical
Insurance
Health history	5	This is one of the most important criteria as it heavily affects the underwriting process, starting even from the medical questionnaire, existing conditions, previous medical exams, etc.
Medical condition	5	This is also at the top of the list in terms of importance as it reflects the current condition of the applicant as determined through the medical questionnaire and potential exams required at the time of the application
Medication	5	Current or previous medication is as important since it can reveal existing medical conditions
Size of policy	3	Medium importance, especially when a very comprehensive/ rich policy with a high sum assured is asked
Other policies	2	Medium-low importance aiming at avoiding enrichment by receiving simultaneous payments from more than one policies
Financial
Income	1	Low importance, as income is not as crucial, especially in the case of health insurance

Created by the authors for the assignment of the level of importance of the criteria

The rationale for using a scale ranging from 1 to 5 for the insurance criteria compared to a 1-to-3 scale for the demographic, lifestyle and financial is that these are the most important criteria for providing health insurance. Demographic, lifestyle and financial criteria are of course needed, however for any combination of the last three the final acceptance decision is determined by the insurability of the interested individual based on his or her insurance profile. Namely, these are his or her health history, (current) medical condition, the size of the policy he or she is applying for and the ownership of other health policies.

The choice of the same importance for some of the criteria within one group is indicated by their contribution to the insurability of the applicant. Such cases are the health history, medical condition and medication within the insurance group, which are the most important determinants for the evaluation of the insurability. Also, age and BMI are the most important within the demographic group, with residence and gender the least important. The latter is primarily because there can be no essential gender differentiation anymore in the European Union. In the lifestyle group, smoking and drinking habits are the most important due to their proven consequences to the health status of an individual, whereas sports and motorcycle riding come second, primarily due to the accidents they may cause.

The weights for the different criteria are then set. These allow the definition of a scoring function/ approach that further allows the assignment of a score to each applicant and the setting of the threshold for acceptance (or rejection), as well as the zone inside which conditional acceptance is granted. To assign global weights, we first attempt to rank the importance of each group. This yields the following ranking (Table 4), with a scale from 1 to 4 (4 being the most important group):

Table 4.

Group importance.

Criteria	Importance	Comment
Demographic	3	The second most important criteria, as age, BMI, etc are also heavily linked to the health of the applicant
Lifestyle	2	The third most important criterion, as lifestyle can lead to certain illnesses or accidents
Insurance	4	The most important criteria, as they reflect the health status of the applicant
Financial	1	The least important criterion for health insurance, as a health schedule matching the available income, can be found

Created by the authors for the ranking of the groups

We then find the global importance of each criterion by multiplying the global importance with the criterion’s partial importance (i.e., within the group it belongs to). We find the weight assigned to each criterion by dividing the global importance by the sum of the global importance scores found (which equals 133). This yields Table 5:

Table 5.

Weights assigned to criteria.

Criteria	Global Importance	Weights	%	Comment
Demographic
Age	9	w1	6.77%	3rd in importance due to the strong link with health
Gender	3	w2	2.26%	7th in importance due to the frequency of use
Occupation history	6	w3	4.51%	5th in importance due to health issues caused
BMI	9	w4	6.77%	3rd in importance due to the strong link with health
Residence	3	w5	2.26%	7th in importance due to the frequency of use
Lifestyle
Smoking status	6	w6	4.51%	5th in importance due to health issues caused
Drinking status	6	w7	4.51%	5th in importance due to health issues caused
Sports	4	w8	3.01%	6th in importance due to accidents caused
Motorcycle riding	4	w9	3.01%	6th in importance due to accidents caused
Military service	2	w10	1.50%	8th in importance due to some link with health
Insurance
Health history	20	w11	15.04%	Most important due to its relevance to health
Medical condition	20	w12	15.04%	Most important due to its relevance to health
Medication	20	w13	15.04%	Most important due to its relevance to health
Size of policy	12	w14	9.02%	2nd most important due to the exposure of the insurer
Other policies	8	w15	6.02%	4th most important due to the exposure of the insurer
Financial
Income	1	w16	0.75%	Last in importance as disproportion may reveal health issues

Authors’ estimates of the weights with the use of the importance levels

To illustrate let us consider health history.

• Health history lies within the insurance group/ category. Insurance carries an importance score of 4.

• Health history carries an importance score of 5 within the insurance group.

• As a result, its total/ global importance score is 20.

• The sum of the importance scores for all factors of all groups is 133.

• Consequently, the weight of health history is equal to 20/133 = 15.04%

The assignment of a level of importance per group and factor/ criterion is based on expert judgment as well as claims experience. Therefore their relevant positions matter more/ are more important than the absolute score assigned. The scales used could be differentiated according to the preference of the insurer.

The available literature explains this by indicating that MCDM methods use the concept of the relative importance of different criteria, which is reflected via a quantitative importance value (weight). Relative importance attempts to capture the verbal expressions that decision-makers use and convert them to numerical values/ ratios. Such verbal descriptions could be “strong importance”, “moderate importance” and “weak importance” leading to a 1–3 scale. This leads to a rank ordering of the criteria. Numerical scores are assigned to indicate the degree to which one decision option is preferred over another. The scores are initially generated for each of the criteria and they are subsequently combined to produce the preference at a model level. The MCDM methods employed in this study (namely MAUT/ MAVT) convert the preference judgments of the decision-makers into quantitative scores (Belton & Stewart, 2002). They thus produce a comprehensive evaluation of each alternative that reflects the preferences of the decision-makers by combining the performance of each alternative according to each of the criteria along with the relative importance of these criteria (Belton & Stewart, 2002).

The health/ medical history is (one of) the most important determinant(s) as evidenced by the underwriting process employed by (private) insurers as well as part of the available research/ literature on insurance underwriting. The latter is based (among others) on the health/ medical history, the age, the type of employment, the geographical region of domiciliation and the lifestyle/ behavioral preferences – if relevant (e.g., smoking status, etc.) of the applicant (Blue Shield of California (2006); Jiahua (2020)).

The aforementioned category breakdown is chosen as part of the generally accepted market practices used by the insurance professionals and has been conveyed as a result of the experience of the authors in the insurance industry. Every insurer can choose its underwriting guidelines; however, the ones presented above comprise a good norm (see for example Table 6 for Blue Cross Blue Shield (2012), Aetna (2010), World Insurance (2008), Health Net (2004), American National Life Insurance Company of Texas (2003) and Affordable Educators (2001)). This is evidenced by the actual underwriting criteria and categories applied by the insurance company whose data and underwriting approach are used in the numerical application.

We then proceed with the assignment of a score for the different tranches/ scales/ categories of each criterion in Table 7 below.

Table 7.

Scoring per criterion.

Criteria	Breakdown	Score	Comment
Demographic
Age (1–5)	0–2 2-18 19–25 26-35 36–45 46-55 56–60 61-65	1 4 3 5 4 3 2 1	New born & infant Child & adolescence Young (accidents) Adult: preferred Adult: low risk Adult: medium risk Adult: high risk Middle-aged
Gender (1)	Male Female	1 1	Evaluation with gender Discriminatory
Occupation history (1–3)	Ultra-white collar White collar Blue collar	3 2 1	Doctor, Lawyer, Prof Office staff All other
BMI (1–3)	18.5< BMI<25 25< BMI<27 27< BMI<30	3 2 1	Preferred Overweight: low risk Overweight: med
Residence (1–3)	Urban Rural	2 3	High frequency Med-Low frequency
Lifestyle
Smoking status (1–5)	No smoking ever No smoking for last 5 yrs No smoking for last 10 yrs Smoking 1–10 cgrts/day Smoking 11–20 cgrts/day Smoking 20+ cgrts/day	5 3 4 3 2 1	Preferred Still some risk Low risk Still some risk Medium risk High risk
Drinking status (1–5)	No drinking at all No drinking for last 5 yrs Drinking 1–2 glasses/day Drinking 3–4 glasses/day Drinking 5+ glasses/day	5 4 3 2 1	Preferred Low risk Some risk Medium risk High risk
Sports (1–5)	High risk sports Medium risk sports Low risk sports Gym No sports	1 2 3 5 4	High accident risk Med accident risk Low accident risk Positive for health Low risk (alone)
Motorcycle riding (1–3)	No Yes	3 2	High accident risk Lower accident risk
Military service (1–3)	Yes – past No – past	3 2	Good health Health issues
Insurance
Health history (1–5)	High risk diseases Medium risk diseases Low risk diseases No risk diseases Accidents No diseases or accidents	1 2 3 4 3 5	High claim risk Medium claim risk Low claim risk Still some claim risk Low claim risk Preferred
Medical condition (1–5)	High risk diseases Medium risk diseases Low risk diseases No risk diseases Accidents No diseases or accidents	1 2 3 4 3 5	High claim risk Medium claim risk Low claim risk Still some claim risk Low claim risk Preferred
Medication (1–5)	High risk diseases Medium risk diseases Low risk diseases No risk diseases Accidents No medication	1 2 3 4 3 5	High claim risk Medium claim risk Low claim risk Still some claim risk Low claim risk Preferred
Size of policy (1–3)	High coverage Medium coverage Low coverage	1 2 3	Consider SA Deductible Coinsurance
Other policies (1–3)	Similar cover Complementary pays first Complementary pays last	1 3 2	Not wanted Preferred paying 1st Paying last
Financial
Income (1–3)	<10xpremium >10xpremium	3 2	Low anti-selection Med anti-selection

Created by the authors for the scoring of the criteria

Please note that the set of criteria employed in our research is the union of the criteria used by the insurers. Most of them are common; exceptions (as can be seen from the online underwriting manuals) are sports/ hobbies, motorcycle riding, military service, size of the policy, other policies and income. We note though that some insurers exclude car racing; hence, although not explicitly mentioned motorcycle racing is possibly excluded. Military service – were not mentioned – may be evaluated at the time of the application. The size of the policy – in the cases not mentioned – is probably evaluated at the time of the application (in terms of sum assured/ covered amount, deductible and/ or coinsurance). The existence of other policies – for the insurers not explicitly mentioning it in their online underwriting manuals – is most likely part of the insurance application as it may require coordination of benefits (specifying which insurer pays first, second, etc.). Income may be part of the financial instead of the medical underwriting; alternatively, it could be part of the questionnaire that the distributor (tied agent, broker, or bancassurance agent) completes with the prospective customer.

To better understand what the high-risk diseases are, some examples can be considered: Alzheimer’s disease, blindness, deafness, kidney failure, organ transplant, multiple sclerosis, HIV/AIDS, Parkinson’s disease, paralysis of a limb, terminal illness, heart attack, cancer and stroke. Other diseases are ranked accordingly to their risk. To achieve uniformity the same categorization is used for health history, medical condition and medication although the diseases could be different in each of them. Medication in particular normally pertains to a list of commonly used drugs, which in turn are linked to their common use, i.e., the disease(s) treated (see for example American National Life Insurance Company of Texas (2003)).

Examples of high-risk sports include automobile or motorcycle racing, underwater diving, aviation (non-commercial), skydiving, hang gliding, parachuting, etc. Other sports are ranked accordingly to their risk (see for example American National Life Insurance Company of Texas (2003)).

6. Evaluation of the insurance application

6.1. Weighting sum method

For the evaluation of an insurance application, the weighting sum method (WSM) is utilized first, being the most straightforward to follow, to assign a numerical value to each candidate that fills in an insurance application (Roszkowska, 2013). Such a value is given by the function (equation):

$$u(s)={\sum }_{i=1}^{16}{w}_i\cdot s_i$$ (1)

where $w_i$ denotes the corresponding weight of Table 5 and $s_i$ denotes the score of Table 7 above, for $i=1\dots 16$. $s$ is the vector of the scores, i.e., $s=(s_1,\dots ,s_{16})$.

The range of values of $u$ is $N_{min},N_{max}$.

• For $u<u_L=N_1$ the application is rejected.

• For $u_L\le u<u_M=N_2$ the application is accepted with exclusions, waiting periods and/ or surcharge.

• For $u_M\le u$ the application is accepted with the standard terms and conditions.

With the aforementioned ranking, we can see that $N_{min}=1.0526$ and $N_{max}=4.2331$.

The levels of $u_L$ and $u_M$ are pretty much determined by the specific underwriting criteria that each insurer wants to implement. These are dictated on one hand by its risk tolerance and risk appetite (as set by the available and required capital for the underwriting risk) that influences the underwriting policy and on the other hand by the commercial policy of the insurance company of interest. The combination of the underwriting policy and the commercial policy could privilege specific customer segments (for example non-smokers and with healthy life-style), thus altering the weights and even shifting the values of $u_L$ and $u_M$.

The advantage of this method is that it can fully blend with the traditional approach that an insurer applies to underwrite its customers. It quantifies the qualitative steps that an underwriter traditionally follows, leaving the flexibility to adjust the weights according to the preferred customer segments. Furthermore, it is easy to explain and comprehend even at a board of directors’ level.

6.2. Numerical application of the weighted sum method

The above Multi-criteria analysis is applied to an actual population of 6,321 insured with a health insurance policy. The scores assigned to each one of them come from Table 8, using their status per the time of their underwriting by the insurance company. Table 8 is an adaptation of Table 7 that reflects the underwriting rules used by the insurance company under examination, to best utilize the available data.

Table 8.

Scoring per criterion – variant for the numerical evaluation.

Criteria	Breakdown	Score	Comment
Demographic
Age (1–5)	0–2	1	New born & infant
	2-18	4	Child & adolescence
	19–25	3	Young (accidents)
	26-35 36–45 46-55 56–60 61-65 (up to 70)	5 4 3 2 1	Adult: preferred Adult: low risk Adult: medium risk Adult: high risk Middle-aged
Gender (1)	Male Female	1 1	Evaluation with age Discriminatory
Occupation history (1–3)	Ultra-white collar White collar Blue collar	3 2 1	Doctor, Lawyer, Prof Office staff All other
BMI (1–3)	18< BMI<29 15< ΒΜΙ<18 & 30< BMI<40 ΒΜΙ<15& 40< ΒΜΙ	3 2 1	Preferred Over/under: low Over/under: med
Residence (1–3)	Urban (Athens, Salonica) Rural (Other)	2 3	High frequency Med-Low frequency
Lifestyle
Smoking status (1–5)	No smoking ever No smoking – application Smoking 1–10 cgrts/day Smoking 11–20 cgrts/day Smoking 20+ cgrts/day	5 4 3 2 1	Preferred Low risk Still some risk Medium risk High risk
Drinking status (1–5)	No drinking at all No drinking for last 5 yrs Drinking 1–2 glasses/day Drinking 3–4 glasses/day Drinking 5+ glasses/day	5 4 3 2 1	Preferred Low risk Some risk Medium risk High risk
Sports (1–5)	High risk sports Medium risk Low risk Gym No sports	1 2 3 5 4	High accident risk Med accident risk Low accident risk Positive for health Low risk (alone)
Motorcycle riding (1–3)	No Yes	3 2	High accident risk Lower accident risk
Military service (1–3)	Yes – present No – present	2 3	Med accident risk Low accident risk
Insurance
Health history (1–5)	High risk diseases Medium risk diseases Low risk diseases No risk diseases Accidents No diseases or accidents	1 2 3 4 3 5	50< Surcharge 20< Surcharge<50 0< Surcharge<20 Surcharge = 0 Not known Surcharge = 0
Medical condition (1–5)	High risk diseases Medium risk diseases Low risk diseases No risk diseases Accidents No diseases or accidents	1 2 3 4 3 5	50< Surcharge 20< Surcharge<50 0< Surcharge<20 Surcharge = 0 Not known Surcharge = 0
Medication (1–5)	High risk diseases Medium risk diseases Low risk diseases No risk diseases Accidents No medication	1 2 3 4 3 5	50< Surcharge 20< Surcharge<50 0< Surcharge<20 Surcharge = 0 Not known Surcharge = 0
Size of policy (1–3)	High coverage Medium coverage Low coverage	1 2 3	SA>1 M DED = 0 OR 600 COINS = 0 OR 0.10 0.5 M< SA<1 M 1000< DED<2000 COINS = 0.25 1 M< SA 5000< DED COINS = 0.40
Other policies (1–3)	Similar cover Complementary pays first Complementary pays last	1 3 2	Not wanted Preferred paying 1st Paying last
Financial
Income (1–3)	<10xpremium >10xpremium	3 2	Low anti-selection Med anti-selection

Entries come from Table 7 with the following adaptations for the numerical example: consideration of urban vs. rural areas (of Greece); assignment of the same value to gender as it cannot be used to discriminate according to the EU Gender Neutral Directive (Official Journal of the Council (The) of the European Union (2004); increase of the maximum acceptance age to 70 years old; introduction of a wider BMI acceptance range; determination of the smoking status based on the application (hence reflecting the smoking status at the time of the application); use of the military service status at the time of the application (thus changing the importance compared to whether the applicant has served or not); health history, medical condition and medication based on the surcharge applied at the time of the application; decision on the size of the policy based on the Sum Assured (SA), Deductible (DED) and Coinsurance (COINS) options offered by the insurer; and addition to the existing, insured (accepted) population of (fictional) individuals exhibiting better or worse scores, so as to test the validity of our approach

Created by the authors for the scoring of the criteria

As all these individuals have been accepted by the insurer, 1,000 more individuals were added (based on the first 1,000 individuals of the population) with their scores altered in some cases for the worst and in some other cases for the better. This was done to allow for candidates that could be rejected as a result of a low total u-value. All the members of the population fall within the insurable population, in terms of age, etc. meaning they are not a-priori rejected. Therefore, it is with the use of the weighting sum method that an attempt is made to determine the acceptance of the candidate individual.

The values of u per candidate individual came out to be from 1.5414 to 4.0226 (Table 9). Looking at the (enhanced) population, it becomes apparent that indeed all insured (or candidates) with high scores in all attributes have high values of u and would thus be accepted. All candidates, from the individuals that were added to the population, that had low scores (especially with regards to health history, medical condition, etc.) exhibit low values of u and would be most likely rejected.

Table 9.

Actual population weighing sums.

Count	Individual	Age	Gender	Occupation History	BMI	Residence	Smoking Status	Drinking Status	Sports	Motorcycle Riding	Military Service Rank	Health History	Medical Condition	Medication	Size of Policy	Other Policies	Income	u -value
1	6631	5	1	3	3	2	5	5	4	3	3	5	5	5	2	2	2	4.023
2	6639	5	1	3	3	2	5	5	4	3	3	5	5	5	2	2	2	4.023
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
94	2323	5	1	3	3	3	4	3	4	3	3	4	4	4	3	2	2	3.549
	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
6684	3043	5	1	3	3	2	4	3	4	3	3	3	3	3	2	2	2	2.984
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
7116	1655	3	1	2	2	2	2	3	4	3	3	2	2	2	1	2	2	2.105
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
7322	6586	1	1	2	1	2	4	3	4	3	3	1	1	1	1	2	2	1.541
7321	6616	1	1	2	1	2	4	3	4	3	3	1	1	1	1	2	2	1.541

Created by the authors with the weighting sum method

The lowest value of u that has been accepted is 2.1053 corresponding to a male insured with a surcharge of 50%. The highest value of u that has been accepted is 3.5489. The highest accepted score with a surcharge is at 2.9850.

Following the above, we can set $u_L=2$ and $u_M=3$ and choose the closest integers to the lowest and maximum accepted u-value. This means that the insurer can accept individuals with a value higher than 3 and reject individuals with a value lower than 2. Applicants with values between 2 and 3 need to be closely reviewed and potentially be directed to undertake medical exams before a final decision can be reached. An interpretation of these findings as well as a sensitivity analysis of the results is offered in Appendix C.1.

We can therefore conclude that the weighting sum method can be used by a health insurer to underwrite the applicants. It can successfully turn a purely qualitative approach into a more quantitative one, it is easy to understand and explain, and can be easily adapted to the standards and preferences of the insurance company. The last attribute allows it to better match the selection criteria of each specific insurance company.

6.3. Promethee

An alternative approach for ranking the candidate individuals is the PROMETHEE method (PROMETHEE, 2013). PROMETHEE is a popular multi-criteria approach aiming to assist decision makers. It belongs to the class of outranking multi-criteria approaches and it provides a ranking of all alternatives. Based on a family of criteria related to multiple choices, PROMETHEE compares all values of the criteria for all alternatives, weights them properly, and ends up in a final score also called “flow”. The highest “flow” indicates a higher position in the final ranking of the alternatives. Despite its popularity and its concreteness in ranking choices, it should be noted that PROMETHEE has a limitation. Namely, the importance of each criterion is always determined by the decision maker. As a result, the respective weights used during the PROMETHEE execution are considered to be subjective.

To apply PROMETHEE a more formal/ rigorous approach is used to determine the weights of each criterion. The method used is the Rank Order Centroid (ROC – see Roszkowska, 2013), which takes the ranks as inputs and converts them to weights for each of the items. The conversion is based on the following formula:

$$w_i=(1/M){\sum }_{n=i}^M(1/n)$$ (2)

where M is the number of items and $w_i$ is the weight for the $i^{th}$ item. To determine the weights, we attempted a single ranking of the criteria, as follows (Table 10):

Table 10.

Single ranking and ROC weights.

Criteria Group	Criteria	Single Ranking	1/Rank	Weights	%	Comment
Insurance	Medical condition	1	1.000	w1	21.13%	Most important due to relevance to health
Insurance	Health history	2	0.500	w2	14.88%	2nd most important due to relevance to health
Insurance	Medication	3	0.333	w3	11.75%	3rd most important due to relevance to health
Lifestyle	Smoking status	4	0.250	w4	9.67%	4th in importance due to health issues caused
Lifestyle	Drinking status	5	0.200	w5	8.11%	5th in importance due to health issues caused
Demographic	BMI	6	0.167	w6	6.86%	6th in importance due to strong link with health
Lifestyle	Military service	7	0.143	w7	5.82%	7th in importance due to link with health
Demographic	Age	8	0.125	w8	4.92%	8th in importance due to link with health
Demographic	Residence	9	0.111	w9	4.14%	9th in importance due to the frequency of use
Demographic	Occupation history	10	0.100	w10	3.45%	10th in importance due to health issues caused
Lifestyle	Motorcycle riding	11	0.091	w11	2.82%	11th in importance due to accidents caused
Lifestyle	Sports	12	0.083	w12	2.26%	12th in importance due to accidents caused
Demographic	Gender	13	0.077	w13	1.73%	13th in importance due to the frequency of use
Insurance	Size of policy	14	0.071	w14	1.25%	14th most important due to the exposure of the insurer
Insurance	Other policies	15	0.067	w15	0.81%	15th most important due to the exposure of the insurer
Financial	Income	16	0.063	w16	0.39%	Last in importance as disproportion may reveal health issues

Authors’ estimates of the weights with the use of ROC

What is still needed in the case of PROMETHEE is to determine the levels for which an application is rejected, is accepted with exclusions, waiting periods and/ or surcharge or is accepted with the standard terms and conditions.

As PROMETHEE does not produce an absolute value but rather a comparative ranking, we will have to put relative values. That means that we will determine the acceptance or not of any new individual based on his or her ranking versus the initial population. Let $I_L$ be the lowest ranking individual of the hypothetical population accepted with exclusions, waiting periods and/ or surcharge and $I_M$ be the lowest ranking individual of the hypothetical population accepted with the standard terms and conditions. For any new candidate individual $I_{New}$ to be evaluated the decision is taken as follows:

• For $I_{New}\prec I_L$ the application is rejected.

• For $I_L\prec I_{New}\prec I_M$ the application is accepted with exclusions, waiting periods and/ or surcharge.

• For $I_M\prec I_{New}$ the application is accepted with the standard terms and conditions.

The symbol $\prec$ denotes the relative ranking between two individuals. This means that for $I_1,I_2$ any two individuals $I_1\prec I_2$ if and only if $I_1$ ranks before $I_2$.

6.4. Numerical application of PROMETHEE

We applied PROMETHEE to the same actual population of insured with a health insurance policy. The scores assigned to each one of them come from Table 8, using their status per the time of their underwriting by the insurance company. However, as our version of PROMETHEE could only handle 999 individuals, we kept the first 900 entries of the accepted insured of the initial population and we enhanced it with another 99 whose scores were altered in some cases for the worse and in some other cases for the better. We did that to allow for candidates that could be rejected. Once more, all the members of the population fall within the insurable population, in terms of age, etc. meaning they are not a-priori rejected. Therefore, it is with the use of PROMETHEE that we will attempt to determine the acceptance of the candidate individual.

The net preference flow $\mathrm{\Phi }$ per candidate individual came out to be from −0.7746 to 0.7244 (Table 11 and Figure 2). Looking at our (enhanced) population, as in the previous method, we realize that indeed all insured (or candidates) with high scores in all attributes have high net preference flows $\mathrm{\Phi }$ and would thus be accepted. All candidates, from the individuals we added to the population, that had low scores (especially with regards to health history, medical condition, etc.) exhibit low net preference flow $\mathrm{\Phi }$ and would be most likely rejected.

Table 11.

Actual population ranking.

Rank	Individual	Phi	Phi+	Phi-
1	6631	0.7244	0.7337	0.0093
2	6629	0.6922	0.7115	0.0193
…	…	…	…	…
11	104	0.1494	0.1569	0.0075
…	…	…	…	…
966	885	−0.4594	0.0778	0.5372
…	…	…	…	…
989	635	−0.6022	0.0423	0.6445
…	…	…	…	…
998	7028	−0.774	0.0181	0.7921
999	7033	−0.7746	0.0165	0.7911

Created by the authors from the indurance company data with PROMETHEE

Figure 2.

Actual population ranking.

Source: Created by the authors from the indurance company data with PROMETHEE

The lowest net preference flow $\mathrm{\Phi }$ that has been accepted is −0.6022. The highest net preference flow $\mathrm{\Phi }$ that has been accepted is 0.1494. The highest accepted net preference flow $\mathrm{\Phi }$ with a surcharge is at −0.4594.

Following the above, $I_L$ and $I_M$ are the individuals exhibiting the above net preference flows $\mathrm{\Phi }$ (i.e., −0.6022 and −0.4594 respectively). We can somehow try to round it and set ${\mathrm{\Phi }}_{\mathrm{L}}=-0.65$ and ${\mathrm{\Phi }}_{\mathrm{M}}=-0.40$, corresponding to the lowest and maximum accepted net preference flow $\mathrm{\Phi }$ (with a surcharge). This means that the insurer can accept individuals with a net preference flow $\mathrm{\Phi }$ higher than −0.40 and reject individuals with a value lower than −0.65. Applicants with values between −0.65 and −0.40 need to be closely reviewed and potentially be directed to undertake medical exams before a final decision can be reached. An interpretation of these findings as well as a sensitivity analysis of the results is given in Appendix C.2.

We thus conclude that PROMETHEE is an MCDM that can be employed by a health insurer to better structure its underwriting process. It delivers a score that can be used as a benchmark for the acceptance, rejection or further examination of an insurance application. It can be adapted to match the specific underwriting criteria that an insurance company may (want to) have in order to address the desired customer segments. The benefits, risks and the risk mitigation that result from the application of PROMETHEE to health insurance underwriting are outlined in Appendix C.3

6.5. Comparison of the two methods

Finally, we try to compare the two methods for the specific population of interest. We first make a note of the modeling part. The scales introduced in the weighting sum method (ranging from 1 to 3 or from 1 to 5–1 the least important and 3 or 5 the most important) depict the importance per group and factor/ criterion within each group. The scales yield an importance level that is somehow proportional to the score assigned. For groups, the scale is relative, whereas for factors the scale is ordinal. Relative means that the ranking/ rating/ scoring is in terms of importance; hence each group is rated/ scored relative to the others. Ordinal means that the ranking/ rating/ scoring is in absolute terms (from a predetermined scale) reflecting how well each factor satisfies a specific interest or purpose; hence more than one factors can have the same score. The final weight introduces proportionality in the global importance per criterion/ factor (see for example Steele et al. (2009) or NCSU (2008)).

When applying PROMETHEE the scale used is relative to produce a single ranking with the application of the Rank Order Centroid (ROC) method, which takes the ranks as inputs and converts them to weights for each of the items.

We elaborate with the use of an example. Please consider health history.

• Health history ranks second (number 2) with the single ranking approach.

• As a result 1/rank = 1/2 = 0.5 for health history.

• The sum of 1/rank for all criteria after the second one (health history) is 2.3807.

• Consequently, the weight of health history as per the ROC approach is the ratio of 2.3807 divided by 16 (the total number of criteria), i.e., 2.3807/16 = 14.88%.

Moving now to the numerical example, please note that as we did not have the full details for all the criteria we introduced, we adapt the weights of PROMETHEE to reflect it. In addition, we limit ourselves to the smaller population of 999 individuals that we used in PROMETHEE, so that we have exactly the same input. This leads to a modified table (Table 12). For its compilation, the rationale of the weights is explained in Table 4.

Table 12.

Modified single ranking and ROC weights for comparison.

Criteria Group	Criteria	Single Ranking	1/ Rank	New Weights	Previous weights	%
Insurance	Medical condition	1	1,000	w1	w1	21,13%
Insurance	Health history	2	0,500	w2	w2	14,88%
Insurance	Medication	3	0,333	w3	w3	11,75%
Insurance	Size of policy	4	0,250	w4	w14	9,67%
Demographic	BMI	5	0,200	w5	w6	8,11%
Demographic	Age	6	0,167	w6	w8	6,86%
Insurance	Other policies	7	0,143	w7	w15	5,82%
Lifestyle	Smoking status	8	0,125	w8	w4	4,92%
Lifestyle	Drinking status	9	0,111	w9	w5	4,14%
Demographic	Occupation history	10	0,100	w10	w10	3,45%
Lifestyle	Motorcycle riding	11	0,091	w11	w11	2,82%
Lifestyle	Sports	12	0,083	w12	w12	2,26%
Demographic	Gender	13	0,077	w13	w13	1,73%
Demographic	Residence	14	0,071	w14	w9	1,25%
Lifestyle	Military service	15	0,067	w15	w7	0,81%
Financial	Income	16	0,063	w16	w16	0,39%

Authors’ estimates of the weights with the use of ROC

As far as the weighting sum method is concerned, the values of $u$ were in a range from 1.6767 to 4.0226. Looking at the (enhanced) population, we realize that indeed all insured (or candidates) with high scores in all attributes have high values of $u$ and would thus be accepted. All candidates, from the individuals that have been added to the population, that had low scores (especially with regards to health history, medical condition, etc.) exhibit low values of $u$ and would be most likely rejected. The highest value of $u$ that has been accepted is 3.5263. The lowest value of $u$ that has been accepted is 2.26316 and is with a surcharge. The highest accepted value with a surcharge is at 2.7820.

Looking at PROMETHEE we realize that it yields almost the same range of net preference flow $\mathrm{\Phi }$, from −0.7687 to 0.6762. The highest net preference flow $\mathrm{\Phi }$ that has been accepted is 0.2119 and corresponds to a different individual. He has a policy with low sum assured and high coinsurance and is thus privileged by the change in the weight of this particular criterion. The lowest accepted net preference flow $\mathrm{\Phi }$ with a surcharge is −0.5517 and the highest accepted net preference flow $\mathrm{\Phi }$ with a surcharge is −0.4406. They are close to the previous ones and are observed at the same individuals, who maintain their relative order. For the remaining the population, we realize that there are some internal moves in terms of the ranking. There do not seem to be important changes in terms of insurability and with a small re-scaling to reflect the new range, they can be captured.

Looking at the two methods, we realize that the individuals with a surcharge are the same (as expected) and in the same order. Moreover, the top and bottom performers are similar, with small variations around the borderlines of acceptance, rejection or further examination. Consequently, by slightly shifting the thresholds to reflect the new values, let’s say for the weighting sum method to a range from 2 to 2.8 and for PROMITHEE to a range from −0.60 to −0.42 the selection yields comparable results. Of course, it is up to/ the choice of the insurer how much it wants to relax or tighten these levels to accept applicants. This comparison shows that the weighted sum method and PROMETHEE yield commensurate/ equivalent results.

6.6. Model calibration to match the desired insured profiles

The sensitivity testing approach described in Section 6.2 and in Appendix C.1 can be used to calibrate the output of the model so that it matches/ aligns with the potential health insurance applicant profiles that the insurance company wishes to accept. In other words, it can perturb the importance per group and per criterion in the group, as well as the score per criterion until the u-values match the preferred profiles. In such a way, the model will match exactly the risk appetite of the insurer. The particulars of the model calibration are presented in Appendix C.4.

6.7. Method limitations

Our research does pose some limitations that pertain to the methods used and the dataset employed. MCDM methods involve the grouping, hierarchical ordering and weight assignment of the relevant criteria. The grouping, ordering and weighting could be highly subjective. The choice of the score threshold used to select the alternatives that rank above it may also be subjective. We realize though that MCDM supports decision-making by combining objective measurement with value judgments, managing subjectivity, and making the process more explicit and transparent (Belton & Stewart, 2002) and assists in converting a purely qualitative framework to a more quantitative framework. A detailed description of the limitations of the MCDM methods used and the ways to overpass them is outlined in Appendix C.5.

An additional limitation may be that the present analysis focuses on full medical underwriting only (moratorium underwriting has not been studied). Consequently, it is considered that applicants have disclosed their complete medical history and filled in a detailed medical questionnaire.

7. Conclusions and further research

In the present manuscript, we introduced Multi-criteria Decision-making methods (the weighting sum method and PROMETHEE) in health insurance/ medical underwriting. We did it by transferring the factors used in underwriting into criteria that we grouped, ordered, weighted, and put scores on. In such a way we assigned a value to each candidate for a health insurance policy by utilizing the information collected through the application he or she filled in and/ or potential medical exams he or she went through. The success of the approach is that we converted a highly qualitative process into a more quantitative one through the appropriate function. The contribution of this research in the field of health insurance underwriting is that it consolidates all available information into one single numerical output that can support an insurer’s decision on the acceptance or rejection or the further investigation of the health coverage application. The latter depends on the interval this output lies. The applicant is normally accepted if his or her score is above a certain level, is rejected if his or her score is below a certain level, and further investigation (e.g., through additional medical exams) and the inclusion of special conditions, and/ or waiting periods, and/ or surcharge may be necessary if his or her score falls between these levels. Consequently, this approach offers a relative evaluation/ comparison method.

As evidenced by the analysis performed, the scoring introduced by MCDM methods aims at facilitating, supporting and enhancing the risk selection process; it does not replace expert judgment. This approach is expected to be applied more and more by insurers as demonstrated by the steps taken by professional consultants. Examples are (i) the call of Deloitte (2021) to reach well-informed underwriting decisions, to base these decisions more on science – introducing rigorous rules and automation along with professional judgment, adapt to the changing nature of risk and if possible predict this evolution; and (ii) the tool that Milliman (2021) developed, which assesses applicants and/ or insured via a relative morbidity score. Assisted by this tool, the underwriting process leads to a decision such as acceptance, rejection, acceptance with exclusions or acceptance with a premium surcharge. The assignment of a single score poses a comparative advantage over the traditional selection that is based on yes-no criteria. More specifically, it turns a purely qualitative and subjective underwriting function to a more quantitative and less subjective one, which allows automation, transparency and homogeneity in the risk (insured) selection. At the same time, it supports the risk management function of the company as it further standardizes the risk assessment and risk selection process. Furthermore, it allows the management to deploy strategies so as to gain a competitive lead, by selecting the (desired) risk profiles that match the risk tolerance and risk appetite of the company.

We have tackled the problem in health insurance underwriting. Future research can be directed towards the investigation of potential information technology (IT) solutions that could automate the process described and make the rejection, acceptance or acceptance with special conditions/ exclusions and/ or surcharge decision less timely and easily reached by the interested individuals.

Appendix A.

A.1 Literature search

The following approach was pursued for identifying the available literature:

• The literature was searched by looking for articles/ papers that combined Multi-criteria Decision Analysis/ Multi-criteria Decision-making and Insurance, Finance and Healthcare, as well as Insurance Underwriting Methods, with the key word combinations mentioned below at both Google and Google Scholar (Table 13):

• [Please insert Table 13 about here]

• It was not limited to health insurance or health insurance underwriting only.

• We introduced a PRISMA diagram (following the advice of the area editor) to explain how the available literature has been captured (Figure 3).

• What we cannot know is if an insurer/ insurance company has already internally implemented such an approach. However, based on the experience of the authors in the insurance industry for about 20 years (1995–2014) the approach has not been implemented by any of the insurance companies they have worked for. This is also the case for the company that provided the data for this paper (in 2017).

Figure 3.

PRISMA diagram for literature reiew search.

A.2 Literature Review

Insurance underwriting methods

A series of articles discusses insurance underwriting methods, distinguished in life, fire (public liability) and motor insurance. They are analyzed below.

1/ Life Insurance

1.1/ The life insurance underwriting methods (for the mortality risk) employed or envisioned (for the future) by insurers, as per a study/ survey conducted by the Society of Actuaries (2018) fall into three categories:

• Traditional Underwriting, which requires detailed personal and medical information, depending on the age and sum assured and may be complemented with medical exams/ records.

• Accelerated Underwriting, which aims at reduced requirements compared to traditional underwriting provided that the applicant meets a series of demographic and health-related standards/ conditions, with potentially higher premium levels.

• Simplified Underwriting, which attempts a stripped underwriting process based only on the information provided by the applicant, resulting in increased mortality experience and thus higher premium.

Moreover, these methods are distinguished in

• Triage, which is the application of a set of rules or algorithms to separate the applicants that can be automatically accepted from the applicants that need to undergo a full or limited (traditional underwriting process).

• Accelerated Underwriting, which involves processes and programs that attempt to expedite the underwriting process for healthy applicants without requiring medical exams.

• Predictive analytics, which models a series of variables to make predictions. Data can come either from the insurer’s data for the customer – if available (based on demographic, financial and health-related characteristics) or from marketing companies for a fee (which are though not always available or reliable).

• Artificial Intelligence (AI)/ Cognitive Computing, which (attempts to) mimic the human (underwriter) functions to perform the underwriting process.

• Algorithmic Underwriting, which uses predictive models or algorithms to categorize the applicants in underwriting classes to facilitate the decision-making process followed by the underwriter.

• Simplified Issue (SI), which makes the underwriting process leaner by lifting certain requirements, with the understanding that the mortality experience will be worse and thus the relevant products will require a higher premium.

• Rules Engines, which employ a series of rules to automatically classify risks or even estimate the price/ rate to be charged, as well as allow to some extent the automated acceptance of candidates for life insurance.

• Electronic data, which employ the relevant (medical) data that are available from a series of sources (such as medical billing data, inpatient drugs, lab values, etc.) to collect information that is necessary for the underwriting process, so as to make it faster.

• Tele-Underwriting, which is a phone data collection/ verification process that is used as input in the underwriting process.

• Other tools/ data, which involve a range of other sources of data that are necessary for the underwriting process, such as (i) medical records from the attending physicians and/ or healthcare providers; (ii) information from entities that do have data relevant to the mortality risk (e.g., Medical Information Bureau (MIB), Motor Vehicle Report (MVR), and Prescription (Rx)); and (iii) from credit/ banking/ financial institutions (e.g., the Fair Credit Reporting Act (FCRA) or other agency/ organization), assuming that the credit standing and the mortality risk are correlated.

The survey covers the current or anticipated approaches. It is expected that in the future more of these tools will be used; however, their impact on the mortality experience of the insurer cannot be currently assessed. The removal of certain requirements could result in higher mortality. Similar methods are recorded by Klein (2013).

None of these approaches mentions Multi-criteria Decision-making methods explicitly. However, it could be that methods similar to ours are implicitly employed by some of them such as predictive analytics (that performs scoring based on demographic, financial and health-related characteristics) and to a lesser extent artificial intelligence and algorithmic underwriting (judged by the descriptions provided in the study).

1.2/ More specifically, over the years, generalizability theory (Burrows et al. (1997)), Fuzzy Decision Systems (Bonisone et al., 2002) and Fuzzy Logic (Horgby et al. (1997)), neural networks (Lin (2009), or combinations of the two (Arora and Vij (2012)), along with machine learning techniques (Li et al. (2018), Boodhun and Jayabalan (2018)), artificial intelligence (Maier et al., 2020) and automated underwriting (Biddle et al. (2018)) have been proposed as approaches of (automated life) insurance underwriting.

2/ Fire public liability insurance in assembly occupancies risk assessment and underwriting auditing with a focus on life safety can be standardized with a scoring scheme that resembles the one used in Multi-criteria Decision-making as per the study of Han (2011). However, the author does not produce the weights and simply explains how they could be produced. This is the closest we have found to our research; it is however incomplete and refers to a different type of insurance. It is not used to perform underwriting, but rather to audit underwriting.

3/ When it comes to motor insurance, artificial neural networks are recommended over linear and logistic models (Kitchens (2009)).

MCDM in finance

Part of the research on the use of MCDM in finance presents the contribution of MCDM in financial decision-making. Spronk et al. (2016) focus on the multi-dimensional character of financial decisions and the employment of MCDA approaches to back them. Their advantages lie in (i) their use in evaluation problems; (ii) the use of quantitative and qualitative criteria in the evaluation process; (iii) the transparency they offer in the evaluation; and (iv) the application of rigorous but flexible scientific methods in the financial decision-making process. Doumpos and Zopounidis (2014) present the contribution of MCDA in addressing the various topics of financial decision-making, as well as the principles of MCDA. More specifically they deploy the applications of MCDA in specific areas, such as banking, credit scoring, portfolio management, investment appraisal and country risk assessment. Zopounidis and Doumpos (2002) highlight the importance of Multi-criteria decision Aid (MCDA) in financial decision-making. A wide range of MCDA methodologies can be used to assist the decision-making in financial problems. The authors provide an in-depth presentation of the contributions of MCDA in finance, emphasizing in real-world applications.

In a different route, Steuer and Na (2003) provide a categorized bibliographic study on multiple criteria decision-making (MCDM) combined with finance. They realize that MCDM approaches are particularly substantial, as finance – especially in its most important and complex managerial aspects – resides within an environment of multiple conflicting objectives. They find that MCDM is used in capital budgeting in a property and liability insurance company as well as in pension fund and manpower planning.

MCDM in healthcare

However, insurance and in particular health insurance are not tackled in any of the aforementioned papers. When it comes to health, there is a series of papers relevant to the application of Multi-criteria decision Analysis in healthcare. A strand of the literature focuses on the literature review of MCDM in healthcare. Frazão et al. (2018) perform a literature review and categorize the articles available in the area of MCDA in health care. They classify the papers by country, type of intervention, type of problem addressed, the definition of the problem, definition criteria and method applied. Adunlin et al. (2015) perform a review and bibliometric analysis for the use of MCDA in health care. They conclude that MCDA has been applied to a broad range of areas in health care, with the use of a variety of methodological approaches. MCDA provides a sound and rigorous approach to decision-making in health care. MCDA offers the potential to overcome the challenges of traditional decision-making tools, especially when making complex decisions that include multiple criteria, simultaneously consider quantitative and qualitative data, and involve multiple stakeholders. Marsh et al. (2014) perform a literature review on the healthcare interventions with the use of MCDA. They assess a series of intervention types; pharmaceuticals, public health interventions, screening, surgical interventions, and devices. Diaby et al. (2013) conduct a bibliometric analysis as well with similar findings. Liberatore and Nydick (2008) pursue a literature review on the analytic hierarchy process (AHP) in medical and healthcare decision-making. They realize that the AHP appears to be a promising support tool for shared decision-making between patient and doctor, evaluation and selection of therapies and treatments, and the evaluation of healthcare technologies and policies.

There is also an array of books/ collective issues that tackle the application of MCDM in healthcare. Marsh et al. (2017), in a collection of articles, attempt to present and tackle the challenges (technical and political) that pertain to the application of MCDA in healthcare decision-making. The articles address (i) the foundations of MCDA in health care; (ii) the applications of MCDA in health care – along with case-studies; and (iii) future directions. In the same wavelength González et al. (2018) have edited an assortment of articles with contributors from Spain.

Finally, there is a series of individual papers that address the use of MCDM in health care. Hansen and Devlin (2021), elaborate on the use of MCDA in healthcare decision-making as it assists in the evaluation of alternatives. They specifically refer to (i) the health technology assessment (HTA), i.e., in drugs, devices, procedures, etc; (ii) the prioritization of patients for surgery; (iii) the prioritization of diseases for research and development; and (iv) the decision-making for treatment licensing. They present the steps involved in MCDA, present counterarguments and discuss a series of questions that pertain to the use of MCDA in HTA. Marsh et al. (2016) report on the good practice guidance on the use of MCDA in healthcare decisions. They address the design, the implementation and the review of MCDA. They illustrate the steps that need to be followed, the incorporation of potential budget constraints and the needed skills and resources. They also draft possible future research directions. Thokala et al. (2016) present (in two reports) the emerging good practices of MCDA in healthcare decision-making. They provide examples of its use in different kinds of decision-making in health care, as well as an overview of the principal methods of MCDA and the key steps involved. They also guide to support the implementation of MCDA, as well as an overview of the skills and resources required to implement MCDA. Their analysis though does not incorporate health insurance.

A series of papers addresses the employment of MCDM in healthcare economics, with the extension of economic evaluation methods such as cost-effectiveness analysis and cost-benefit analysis. These approaches may be used to reach healthcare investment decisions or designing/ enlarging public health insurance schemes (see for example Jit (2018) and Norman et al. (2018)).

There are also country-specific or aspect-specific articles addressing the application of MCDM in healthcare. Pereira et al. (2020) employ MCDA to rank nine of the European health systems with Beveridgian financing to identify the weaknesses of the Portuguese National Health Service and recognize potential best practices. Öztürk et al. (2020) use MCDA – and in particular MCDA4HTA - in HTA decision-making, judging that it secures the commitment of multi-disciplinary stakeholders and it comprises a tool for reaching good decisions for the public. They apply it in the case of Turkey to study the role of peritoneal dialysis in renal care. Defechereux et al. (2012) look at the MCDA as a means for healthcare priority setting in Norway. The authors acknowledge that the tax-based health service guarantees all citizens health care in case of a severe illness, a proven health benefit, and proportionality between need and treatment. Consequently, their study compares the values of the country’s health policymakers with these three official principles. They find that Norwegian policy-makers’ values are in agreement with principles formulated in national health laws and conclude that Multi-criteria Decision approaches may provide a tool to support explicit allocation decisions.

MCDM in (health) insurance

(Health) insurance underwriting does not seem to be captured in any of the above articles either. Even though since the initiation of this research (in 2018), there have been some articles that use MCDM in certain insurance (or health insurance) related aspects, health insurance underwriting is not among them. The word “health” has been put in parentheses to indicate that the relevant literature captures the entire insurance activity and not only health insurance.

A strand of the literature addresses the (optimal) selection of an insurance plan. Pattnaik et al. (2021) propose an MCDM model (fuzzy MCDM combined with the technique for order preference by similarity to ideal solution - TOPSIS) to facilitate the (online) purchase of life insurance coverage in India. To do so, they rank 12 insurance companies that offer online term (life) plans. Guo (2017) uses MCDA to address health insurance for foreigners in the Czech Republic. In his study, he solves the problem of the selection of the optimal health insurance plan for foreigners visiting the Czech Republic. Although his research is relevant to health insurance, he does not deal with the underwriting process.

A part of the literature addresses motor insurance. Esfandabadi et al. (2020) employ MCDA approaches (a two-phase process based on the fuzzy Delphi method - FDM and fuzzy analytic hierarchy process - FAHP) to identify and prioritize important risk factors relevant to the personal and behavioral attributes of the drivers on top of the vehicle characteristics. The introduction of such factors can improve the accuracy and fairness of pricing in Iran which is based only on the vehicle characteristics for comprehensive motor insurance. The latter is crucial for the risk selection process and thus for the financial position of the insurers in the country. Heras et al. (2015) realize the multi-objective nature of bonus-malus systems insurance as it attempts to meet three objectives; fairness, toughness and (dis)equilibrium. They represent these objectives mathematically with the use of linear problems and apply multi-objective algorithms to find the values of the objectives, as well as the best alternative.

There is a series of articles on insurance company corporate issues. Gharizadeh Beiragh et al. (2020) assess the sustainability performance of insurance companies with MCDM. Their sample consists of 14 Iranian insurance companies and for the evaluation they used principal component analysis and analytical hierarchy process over 8 economic, 3 environmental and 4 social indices. Rubio-Misas and Gómez (2015) use MCDM (cross-frontier methodology based on data envelopment analysis – DEA) to assess the relative efficiency of stock (owned by stockholders) and mutual insurance companies (owned by policyholders). They find that the efficiency structure hypothesis yields that both organizational structures have equal efficiency after controlling for production technology and business mix; whereas the expense preference hypothesis indicates that stock insurance companies will be more efficient than mutual insurance companies.

An article was found relevant to insurance coverage. Shahabi et al. (2021) use MCDM (a qualitative study complemented with an analytical hierarchy process (AHP)) to draft recommendations that will improve the insurance coverage for physiotherapy services in Iran.

Going to health insurance underwriting, Bly (2004) presents international medical underwriting approaches, along with their impact on profitability and compares them with the approach followed in the USA. He finds that the current international approaches to medical underwriting include extensive use of riders to limit coverage for specific conditions, reliance upon a medical professional judgment for rating purposes, and application of life insurance underwriting guidelines or US medical underwriting guidelines. While the use of these methods could be justified by the fact that these might be the only available tools for international underwriters, the reality of the inappropriateness of their use for medical rating purposes remains unchanged. MCDM is not among the methods applied.

In summary, we realize that the use of MCDM in insurance focuses on the (optimal) selection of an insurance plan; the identification and prioritization of important risk factors relevant to the personal and behavioral attributes of the drivers; the valuation of the objectives of the bonus-malus systems; the assessment of the sustainability of the performance of insurance companies; the assessment of the relative efficiency of stock (owned by stockholders) and mutual insurance companies (owned by policyholders); and the insurance coverage for physiotherapy services. Furthermore, the literature on medical underwriting unveils the approaches employed, which are the extensive use of riders to limit coverage for specific conditions; the reliance upon a medical professional judgment for rating purposes; and the application of life insurance underwriting guidelines or US medical underwriting guidelines. Consequently, when it comes to health insurance underwriting we realize that MCDM is not among the established approaches.

MCDM methods

The identified literature – as presented above - indicates that there is room for the use of MCDM in health insurance underwriting. The spectrum of MCDM methods is presented by Velasquez and Hester (2013). The authors describe the methods that have been developed over the years, examine their advantages and disadvantages and explain how their applications relate to strengths and weaknesses. Mourmouris (2006) paves a good path for setting the methodology, the criteria, the weights and scoring and finally applying MCDM for the evaluation. Although he uses it for a different problem compared to ours, it can still be followed due to its detailed presentation.

Finally, there seems to be room and need for automated life insurance underwriting, as evidenced by the survey conducted by Deloitte - engaged by the Society of Actuaries’ Marketing and Distribution Section Council, the Product Development Section Council and the Committee on Life Insurance Research (Batty and Kroll (2009)). MCDM can be used to automate health insurance underwriting.

The above indicates that the contribution of our paper is twofold, as on one hand it introduces MCDM in health insurance underwriting and on the other hand it sets the ground for automation in health insurance underwriting.

Appendix B.

B.1 Details of the stages and the stakeholders of the MCDM process

The first stage has two sub-stages, namely the identification and the structuring of the problem. The former indicates that the problem is not (always) well-defined; thus part of the process is to define the problem to be solved. The latter has to do with the formation of the problem out of the potential divergent thoughts of the decision-makers and the complex issues that may be inherent and their expression in a way that will allow the decision process to move forward.

The second stage consists of two sub-stages also. These are the building and the use of the model. The former pertains to the development of a model that can be used to solve the problem and achieves convergence of the thoughts of the decision-makers. It may unveil issues that stimulate divergent opinions anew, which will lead through to the constructive evaluation of alternative options. The latter has to do with the actual use of the model to produce results that can facilitate the decision process.

The last stage has to do with the employment of the model output to make an action plan relevant to the desired decision (making). However, even at this stage the process may necessitate the return to a previous stage and its revision as the decision-making process is highly dynamic – especially if it is repeated. The aforementioned process is iterative and a return to a previous stage may take place at any point in time (Belton & Stewart, 2002).

The stakeholders of the process besides decision-makers (may) include clients, sponsors, (potential) opponents, facilitators and analysts. The aforementioned iteration is not only inter-stage but also intra-stage in an attempt to amalgamate the interests and/ or influences of these internal and external stakeholders. The MCDM process emphasizes the building and the use of the model. The various MCDM methods differ in terms of the particulars of the model, the input it needs and the way it is put at work. They resemble in the sense that they all require the prior selection of the available alternatives/ choices, the criteria/ objectives/ standards/ factors that are used for the assessment of the alternatives and the measurement of the relative significance of the criteria. However, they differ in the way they combine this input to accommodate the decision-making (Belton & Stewart, 2002).

B.2 Elimination criteria

The applicant elimination criteria employed are:

• Demographic criteria

  • Age: applicants outside a certain range are rejected; normally of age less than one-month-old or older than 65 (or another age up to 70) years old.
  • Occupation history: certain professions are not covered at all; hence, if an interested individual applies, then he or she will be rejected.
  • BMI (Body Mass Index = Weight/ Height² → could be replaced by Weight and Height): certain ranges of BMI are not accepted for health insurance; these are index values less than 18.5 and higher than 30. Depending on the insurer they can go down to less than 15 and higher than 40. Even in these cases, BMI values higher than 30 are indicating higher risk.
• Lifestyle criteria

  • Sports: certain sports could lead to rejection.
  • Motorcycle riding: (not always) motorcycle riding could lead to rejection; if not it could lead to exclusions or longer waiting periods due to an accident.
  • Military service: during military service coverage is not offered and even if a policy is (or has been) issued it could be suspended.
• Insurance criteria

  • Health history: certain illnesses could lead to rejection and pre-existing conditions are excluded – even if the applicant is accepted.
  • Other policies: occasionally when similar policies are in place coverage is not offered, as it could lead to double coverage.
• Financial criteria

  • Income: if income is too low compared to the corresponding premium, then the applicant may not be accepted.

Even if an individual passes the elimination criteria, he or she could still be rejected after the evaluation takes place.

B.3 Evaluation criteria

The applicant evaluation criteria used are:

• Demographic criteria

  • Age: depending on the age, medical exams may be asked. The results of these exams are used for the evaluation of the insurance application.

    • Usually, until the age of 50, a medical questionnaire suffices as a first step. Certain answers in the medical questionnaire could also lead to medical tests.
    • Medical exams are required after the age of 50 and until the 65^th year of age (or the highest year of age accepted). Usually, these exams are of increasing number and breadth for every 5 years of age.
    • An indicative (but more or less standard) list of medical exams included for the ages up to 60 are pathological examination, complete (full) blood count – ESR, urinalysis, blood sugar, urea, creatinine, cholesterol, HDL, gamma – GT, triglycerides. For ages higher than 60 additional medical exams may be required, such as PSA.

  • Gender: it cannot be a reason to reject or differentiate anymore in the European Union as per a Gender Neutral Directive (Official Journal of the Council (The) of the European Union (2004)), effective for insurance as of December 21 2012 (European Commission (2012)); however it is used for evaluating the global condition of the applicant.

  • Occupation history: certain professions – even from the past – could lead to waiting periods or surcharges due to increased risk for the insurer.

  • BMI (Body Mass Index = Weight/ Height² → may be replaced by Weight and Height combined/ together): if coverage is offered, then certain BMI values could lead to exclusions or surcharges. Being overweight (especially) or underweight could lead to increased incidents of certain diseases (e.g., cardiovascular disease in the first case and nervous problems in the second). It may also prolong the recovery time. Historical fluctuation of BMI could also lead to such deviations from the standard terms and conditions.

  • Residence: The place of residence is considered in the evaluation process. It is usually believed that individuals from rural areas exhibit a better health status than the ones from urban areas. This is because it reflects their lifestyle and nutrition habits, which in rural areas are thought to be somehow healthier. Exceptions are areas with a proven concentration of medical incidents, such as industrial areas that exhibit a high frequency of cancer occurrences.

• Lifestyle criteria

  • Smoking status: it describes the smoking history of the applicant, i.e., not only whether he or she smokes at the time of the application, but also what he or she did in the past. Heavy smokers could be rejected. If not, longer waiting periods and/ or surcharges could apply.

  • The latest trend is that smokers are charged a higher premium vs. non-smokers.

  • However, it has to be acknowledged that smoking history is not always recorded. It is rather the smoking/ non-smoking status. Smokers are asked to declare the number of cigarettes they smoke per day.

  • Drinking status: similar principles to smoking status apply, although not as common. As a consequence, it is sometimes alcoholism that is among the standard exclusions of the insurance policy.

  • Sports: certain sports could lead to exclusions from coverage – especially in case of an accident – or surcharge. This stems from the risk associated with the sport.

  • Motorcycle riding: could lead to exclusions in case of accident or to a surcharge.

  • Military service: exemption from military service could reveal a medical condition that may lead to rejection, exclusions, longer waiting periods or surcharge. This is seldom declared though. If the application is filed during the military service, then exclusions or waiting periods could apply as well.

• Insurance criteria

  • Health history: certain older illnesses or accidents etc could lead to waiting periods, exclusions, surcharges, etc.

  • Medical condition: the medical condition at the time of the application, as determined by the medical questionnaire and the possible medical exams could lead again to waiting periods, exclusions, surcharges, etc.

  • Medication: current and previous medication reveals known or potential health issues and could lead to medical exams, waiting periods, exclusions, surcharges, etc.

  • Size of policy: the size of the policy is used to determine the premium, but also the final acceptance. For example, certain profiles could be directed to smaller sum assured or higher deductible and/ or coinsurance.

  • Deductible and coinsurance, i.e., the level of participation of the insured in case of a claim is also important. This is considered as part of the size of the policy but could also be treated separately.

  • Other policies: the existence of other complementary policies may be used to determine a level of deductible, coinsurance or even coordination of benefits among the different providers.

• Financial criteria

  • Income: it is evaluated next to the premium and proof may be asked. Also, if income is low compared to the premium the continuity of the policy can be at stake.

B.4 Particulars of the MCDM methods

The MCDM methods display the following attributes:

• Cost-benefit analysis: this method assesses only the costs and the benefits of the alternatives on a monetary basis to select the alternative with the optimal cost-benefit relation (Fülöp, 2005).

• Elementary methods: they are simple to use and comprehend and require no computational support. They are employed when there is a single decision-maker, a relatively small number of alternatives and a relatively small number of criteria. Pros and cons analysis, maximin and maximax methods, conjunctive and disjunctive methods and the lexicographic method lie within the elementary methods. For example, pros and cons analysis is a purely qualitative method that compares the advantages and disadvantages of each alternative to select the alternative with the strongest advantages and weaker disadvantages (Baker et al., 2001; Fülöp, 2005).

• Multi-attribute utility/ value theory approaches involve the weighting of the criteria so that the relative importance of the criteria is captured when the scores assigned come from a dimensionless scale. They transform performance values of the alternatives based on a series of criteria that can be factual, i.e., objective and quantitative as well as judgmental, i.e., subjective and qualitative to a common dimensionless scale. The (utility) function(s) are employed to assign a higher (utility) value to the more preferred raw performance value. The MAUT/ MAVT methods manage to aggregate different criteria into one function/ value that needs to be optimized. Consequently, the mathematical relations of this combination of criteria are considered. They allow the trade-offs between the various criteria (Fülöp, 2005; Keeney & Raiffa, 1976). The weighting sum method (WSM), the generalized means approach, and the analytic hierarchy processes (AHP) are MAUT/ MAVT methods.

• Outranking methods are based on the idea that one alternative outranks another alternative if on a material portion of the criteria the former performs at least as good as the latter (concordance condition) and at the same time its underperformance on the remaining criteria is acceptable (non-concordance condition). For each pair of alternatives, outranking methods determine whether one alternative outranks the other and combine them to reach a complete or partial ranking. Compared to MAUT approaches one can see that they may not lead to a single best outcome but a series of qualifying outcomes (Fülöp, 2005; Roy, 1968). Examples of outranking methods are ELECTRE and PROMETHEE.

• Group decision-making considers the ensemble of the different preferences of multiple decision-makers on a set of alternatives to reach one single collective preference. All individuals that take part in a group decision process are interested in finding a solution to a common problem. These individuals usually exhibit different skills, experiences and knowledge with regard to the criteria that are relevant to the problem they wish to solve (Fülöp, 2005).

Appendix C.

C.1 Interpretation and sensitivity of the weighted sum method

The lowest value of $u$ that has been accepted is 2.1053 corresponding to a male insured with a surcharge of 50%. This is most likely an outlier, in the sense that the said individual most likely had a serious health problem at the time he applied for health insurance. In addition, he seems to be a heavy smoker and overweight. These characteristics led to such a low value. All the other insured that have a value around this area seem to have more than one low score and in all cases a surcharge, indicating an existing health issue. The highest value of $u$ that has been accepted is 3.5489 and corresponds to a female individual with high scores in all fields. We do not observe higher values in the insured population as we did not have access to the actual insurance application to properly score the health history, the medical conditions and other important fields. The highest accepted score with a surcharge is at 2.9850.

As a sensitivity test, we increased the importance of occupation history to 3 and residence to 2 (both increased by 1) and recalculated the $u$-values. The range of values changes to the interval 1.5612–3.9568. The lowest accepted individual with a surcharge has now a value 2.1007 and corresponds to the same individual as before. The highest accepted individual has now a value of 2.9640 and is again the same individual as before. These findings indicate that our choice can stand a perturbation/ shift of the parameters.

The lowest net preference flow $\mathrm{\Phi }$ that has been accepted is −0.6022 corresponding to a male insured with a surcharge of 25% (as our population is smaller this time he is different from the one in the weighting sum method). This is most likely an outlier, in the sense that the said individual had a serious health problem (as implied by the surcharge) at the time he applied for health insurance. In addition, he seems to be a regular smoker and overweight. These characteristics led to such a low value. All the other insured that have a value around this area seem to have more than one low score and in all cases a surcharge, indicating an existing health issue. The highest net preference flow $\mathrm{\Phi }$ that has been accepted is 0.1494 and corresponds to a female individual with high scores in all fields (again different from the one in the weighting sum method). We do not observe higher values in the insured population as we did not have access to the actual insurance application to properly score the health history, the medical conditions and other important fields. Moreover, the introduction of the enhanced population of individuals with extremely high scores probably overshadowed the actual population. The highest accepted net preference flow $\mathrm{\Phi }$ with a surcharge is at −0.4594. We only have four such cases, most likely due to the significantly lower population.

As a sensitivity test, we increased the importance of occupation history over residence and reran PROMETHEE. The highest net preference flow $\mathrm{\Phi }$ that has been accepted is 0.1479 and corresponds to the same individual as before. The lowest net preference flow $\mathrm{\Phi }$ with a surcharge is −0.7757 and the highest 0.7298. They correspond to the same individuals as before. The output remained globally close to the previous one, with no changes in insurability, indicating that our choice can stand a perturbation of the parameters.

C.3 Application of PROMETHEE to health insurance underwriting: benefits, risks and risk mitigation

The “colored” approach introduced by PROMETHEE allows for a visual interpretation but also a commercial application of the MCDM-assisted underwriting function. More precisely, the individuals whose net preference flow $\mathrm{\Phi }$ is greater than or equal to ${\mathrm{\Phi }}_M$ and corresponds to the upper “green” part of the PROMETHEE output (Figure 2) are the applicants that are accepted (without any special conditions or surcharge); the individuals whose net preference flow $\mathrm{\Phi }$ is lower than or equal to ${\mathrm{\Phi }}_L$ and corresponds to the lower “red” part of the PROMETHEE output (Figure 2) are the applicants that are rejected. The individuals whose net preference flow $\mathrm{\Phi }$ is between these two values are the applicants for whom the further (medical) examination is required before they are accepted (most likely with surcharge and/ or special conditions) or rejected. This category can be “colored”/ characterized as “yellow”. In such a way the output of PROMETHEE allows for a clear visual display: green – accepted; yellow – additional examination required before a decision is reached, and red – rejected. The latter is easy to commercialize towards distributors and customers and allows even for the online distribution of health insurance or tele-underwriting, i.e., remote underwriting that does not require the use of a paper application; the underwriter via a phone call or a chat application can complete the particulars of the applicant; alternatively, the applicant can fill in digitally such an application himself or herself and be informed of the outcome (acceptance, further investigation, rejection) immediately.

The benefits for the insurer are probably straightforward; (i) the underwriting process can be digitized and automatized; (ii) the assessment can be easy and fair; (iii) the result of the assessment can be immediate for most of the applications (acceptance or rejection), leaving only a few cases for manual evaluation; (iv) the outcome can be visually displayed with the “colored” approach (green, yellow, red) in a way that all stakeholders (in particular distributors and prospective customers) can understand; and (v) the acceptance threshold, as well as the accepted applicant profiles are aligned with the risk appetite/ tolerance of the company. The risks that the insurer may face are that (i) a fully automated process may falsely immediately accept or reject certain profiles (the interim is not considered as risky, since the manual evaluation process will determine whether the applicant should be accepted or rejected); (ii) the limitations (or shortcomings) of the proposed method(s) (presented in Section 6.6.) may influence the outcome of the underwriting process; (iii) the subjectivity in the determination of the importance of the groups and the criteria, and the score per criterion may influence the acceptance or the rejection of the applications, depending on the prudency of the experts that determine them; and (iv) competitors may decode the importance as well as the scores of the underwriting criteria that the insurer uses, especially if online applications along with the decision are available. These risks can be mitigated by (i) calibrating the model(s) to reflect the desired or the already accepted risk profiles periodically or when new information arrives; (ii) using more than one method to offset the drawbacks of each particular method; (iii) reaching a consensus on the importance of the groups and the criteria, and the score per criterion among experts - internal and external; and (iv) adapting the online process periodically to incorporate new information, improve accuracy and lead competition.

C.4 MCDM method calibration

Following the introduction of MCDM methods in medical insurance underwriting, one question is how to determine what profiles the company wishes to accept. This can be established with the following steps.

1. The underwriting department has to carefully study beforehand the profiles that have been accepted, rejected or accepted with special conditions/ exclusions and/ or surcharge with the traditional qualitative process and potentially remove any outliers, i.e., individuals that should not have been accepted, rejected or accepted with special conditions/ exclusions and/ or surcharge.

2. The actuarial department needs to produce the frequency, the severity and the loss ratio per group and criterion to be able to compare the various accepted profiles (to the highest possible granularity).

3. The risk management department needs to produce the Solvency Capital Requirement (SCR) contribution per group and per criterion, using the frequency, severity and loss ratio information.

4. The management of the company (e.g., Executive Committee, Board of Directors, etc) needs to decide the total acceptable SCR that is generated from this kind of risk (insurance risk) and the desired SCR contribution per group and per criterion. Please note that the management may accept that the desired insured profiles are aligned with the already accepted/ insured population.

5. This process is repeated backward to deliver the desired risk profiles that match the risk tolerance and risk appetite of the company.

These steps secure that the insurance company will accept, reject or accept with special conditions/ exclusions and/ or surcharge applicants that fulfill the targeted risk profile. At this point in time, the described calibration (via the perturbation of the importance and the scores) can be applied to produce the desired u_L and u_M levels.

If the insurer does not wish to perturb each importance and each score level separately, then it can group together criteria that it wishes to move en bloc. In this way, it can shift them up or down at the same time. To decide which criteria will move together, it can look at their correlations; a high correlation is indicative of a potential simultaneous movement. However, as independence of the criteria is one of the hypotheses/ prerequisites of MCDM, a high correlation could mean that the insurer may need to reconsider these criteria.

A calibration of PROMETHEE to match the profiles that the insurance company wishes to accept, reject or accept with special conditions/ exclusions and/ or surcharge can be performed in pretty much the same way as the calibration of WSM. The only difference is that instead of the u-values the values of the net preference flow Φ are used.

C.5 MCDM limitations and ways to address them

When it comes to the methods employed, we see that MCDM methods do pose some limitations that need to be taken into consideration when applied. More specifically, on one hand, the weighting sum method (i) does not offer the possibility to integrate multiple preferences; and (ii) evaluates only one dimension. Nevertheless, it is a very simple computation process and is appropriate for single-dimension problems (see for example Siksnelyte-Butkiene et al. (2020)). As mentioned earlier, the advantage of this method is that it readily quantifies the qualitative process of customary health insurance underwriting. On the other hand, PROMETHEE (i) may be applied when the decision-maker can express on a ratio scale both the preference and the importance between two actions on a given criterion; (ii) the criteria weights indicate tradeoffs; (iii) the criteria need to lead to meaningful differences in the evaluations; (iv) it is not possible to consider discordance at the construction of the outrank relations; (v) when adding or deleting an action the relative position of the two actions in the preorder may change and if this action is dominated by all others or is equal to another action then the preorders do not change but the final decision may be affected; (vi) the computation process can be quite long; (vii) calculations may be complex, hence may be good for experts only (see for example De Keyser and Peeters (1996) and Siksnelyte-Butkiene et al. (2020)). As the importance of each criterion is always determined by the decision-maker, the respective weights used during the PROMETHEE execution are considered to be subjective. Nevertheless, the approach is useful when the harmonization of the alternatives is difficult; it can produce results with both qualitative and quantitative information; it can incorporate uncertain and fuzzy information (see for example Siksnelyte-Butkiene et al. (2020)). To counterbalance the limitations of the different approaches, the employment of more than one method at the same time, and the performance of sensitivity analysis by perturbing the weights of the criteria used (as illustrated in Sections 6.2 and 6.6) is recommended.

Besides the aforementioned limitations, the approach followed in this manuscript is supported by the relevant literature, which indicates sensitivity analysis (Dodgson et al. (2009), Martin and Mazzotta (2018), Martins et al. (2016), Monat (2009), Pinazo et al. (2021), Steele et al. (2009)) and calibration (Dodgson et al. (2009), Steele et al. (2009)) as means to secure the strength of the output of the method(s) employed. Even though scaling issues and approaches have also been reported/ addressed (Dodgson et al. (2009), Martin and Mazzotta (2018), Martins et al. (2016), Monat (2009), Steele et al. (2009)), they are tackled with careful scale selection and (re)calibration. Nevertheless, the available research concludes that the assignment of scores/ weights needs to be done in such a way that it captures the choices of the decision-maker(s) (Martin and Mazzotta (2018)). Different methods may lead to different results; they need to be adapted to match the objectives and preferences of the decision-maker(s) (Dodgson et al. (2009), Martin and Mazzotta (2018), Steele et al. (2009)). In determining the scales/ weights we have applied these recommended practices; (our) expert judgment was matched as indicated.

Disclosure statement

No potential conflict of interest was reported by the author(s).