Time Consistency of the Mean-Risk Problem

When dealing with dynamic optimization problems, time consistency is a desirable property as it allows one to solve the problem efficiently through backward recursion. The mean-risk known be inconsistent when considered in its scalarized form. However, left original bi-objective form, turns out satisfy more general that seems better suited vector problem. In “Time Consistency of Mean-Risk Problem,” Ková?ova and Rudloff introduce set-valued version famous Bellman principle show does it. Then, upper image, set contains efficient frontier on boundary, recurses time. present conditions under which this recursion can exploited directly compute solution spirit programming. This opens door for new branch mathematics: multivariate