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

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-ob...

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Bibliographic Details
Published inOptimization Vol. 71; no. 14; pp. 4213 - 4241
Main Authors Yang, Ben-Zhang, He, Xin-Jiang, Zhu, Song-Ping
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 09.12.2022
Taylor & Francis LLC
Subjects
Criteria
equilibrium
Game theory
Investment strategy
Mathematical analysis
mean-variance portfolio problem
Merton's problem
Multiple objective analysis
Optimization
Risk management
time-inconsistency control
utility
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ISSN0233-1934
1029-4945
DOI10.1080/02331934.2021.1939339

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Summary: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 in the literature before.
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content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2021.1939339