Optimal portfolio selection with VaR and portfolio insurance constraints under rank-dependent expected utility theory

This paper investigates two optimal portfolio selection problems for a rank-dependent utility investor who needs to manage his risk exposure: one with a single Value-at-Risk (VaR) constraint and the other with joint VaR and portfolio insurance constraints. The two models generalize existing models under expected utility theory and behavioral theory. To obtain explicit optimal solutions, the martingale method, quantile formulation, and relaxation method are used. We have specifically identified an equivalent condition under which the VaR constraint is effective. A numerical analysis is carried out to demonstrate theoretical results, and additional financial insights are presented. We find that, in bad market states, the risk of the optimal investment outcome is reduced when compared to existing models without or with one constraint.