2020/05/14 by Yang, Ben-Zhang, He, Xin-Jiang, Zhu, Song-Ping
#FOS: Economics and business #Mathematical Finance (q-fin.MF)
paper · doi:10.48550/arxiv.2005.06782
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.