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We consider the problem of choosing a portfolio that maximizes the cumulativeprospect theory (CPT) utility on an empirical distribution of asset returns. Weshow that while CPT utility is not a concave function of the portfolio weights,it can be expressed as a difference of two functions. The first term is thecomposition of a convex function with concave arguments and the second term acomposition of a convex function with convex arguments. This structure allowsus to derive a global lower bound, or minorant, on the CPT utility, which wecan use in a minorization-maximization (MM) algorithm for maximizing CPTutility. We further show that the problem is amenable to a simpleconvex-concave (CC) procedure which iteratively maximizes a localapproximation. Both of these methods can handle small and medium size problems,and complex (but convex) portfolio constraints. We also describe a simplermethod that scales to larger problems, but handles only simple portfolioconstraints.

Portfolio Optimization with Cumulative Prospect Theory Utility via Convex Optimization