Seminar by Zhenyu Cui (Stevens Institute of Technology)
Title: Optimal investment with probability distortion and non-concave utility
Abstract: In this paper, we consider the optimal investment problem with probability distortion (or weighting) and general non-concave utility functions (e.g. S-shape utility). This generalizes and nests some previous literature on mathematical behavior portfolio choice, in which either the probability distortion or the non-concave utility, but not both, is considered. We propose a novel relaxation method to solve it utilizing the concave envelope of the utility function and by relaxing the probability distortion effect through concavification. We establish sufficient conditions to guarantee the existence and uniqueness of the optimal solutions. We apply our method to solve some representative problems scattered in the literature in a unified fashion, and also to the hedge fund profit sharing problem with probability weighting.