Algorithm 2 GBC for Portfolio Learning

Simulate log-returns $W^{\left(i\right)}\mid {\omega }^{\left(i\right)}\sim N((1-{\omega }^{\left(i\right)})r_f+{\omega }^{\left(i\right)}\mu ,{\sigma }^2{\omega }^{\left(i\right)}2)$   Calculate corresponding utilities $Z^{\left(i\right)}=U\left(W^{\left(i\right)}\right)$   Learn $F_{Z_{\omega }}^{-1}$ with a quantile NN   Find the optimal portfolio weight ${\omega }^{★}$ via $$E\left(Z_{\omega }\right)=\sum _{i=1}^N{F}_{Z_{\omega }}^{-1}\left(u_i\right)\to \underset{\omega }{\mathrm{maximize}}$$