Continuous time mean-variance-utility portfolio problem and its equilibrium strategy

Ben-Zhang Yang, Xin-Jiang He and Song-Ping Zhu

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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.

Date: 2020-05, Revised 2020-11
New Economics Papers: this item is included in nep-rmg and nep-upt
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