Continuous time mean–variance–utility portfolio problem and its equilibrium strategy. (9th December 2022)

• Record Type: Journal Article
• Authors: Yang, Ben-Zhang; He, Xin-Jiang; Zhu, Song-Ping
• Is Part Of: Optimization. Volume 71:Number 14(2022)
• Page Start: 4213
• Page End: 4241
• Publication Date: 2022-12-09
• Subjects: Merton's problem -- mean–variance portfolio problem -- equilibrium -- time-inconsistency control -- utility; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1939339
• Languages: English
• ISSNs: 0233-1934

Abstract

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 in the literature before.