Continuous time mean-variance-utility portfolio problem and its equilibrium strategy
Abstract
In this paper, we propose a new class of optimization problems, which maximize the terminal wealth and accumulated consumption utility subject to a mean variance criterion controlling the final risk of the portfolio. The multiple-objective optimization problem is firstly transformed into a single-objective one by introducing the concept of overall "happiness" of an investor defined as the aggregation of the terminal wealth under the mean-variance criterion and the expected accumulated utility, and then solved under a game theoretic framework. We have managed to maintain analytical tractability; the closed-form solutions found for a set of special utility functions enable us to discuss some interesting optimal investment strategies that have not been revealed before in literature.
Keywords
Cite
@article{arxiv.2005.06782,
title = {Continuous time mean-variance-utility portfolio problem and its equilibrium strategy},
author = {Ben-Zhang Yang and Xin-Jiang He and Song-Ping Zhu},
journal= {arXiv preprint arXiv:2005.06782},
year = {2020}
}