Dynamic Portfolio Selection for Nonlinear Law-Dependent Preferences

• 成果类型: Article; Early Access
• 署名作者: Liang, Zongxia; Xia, Jianming; Yuan, Fengyi
• 署名单位: Tsinghua University; Chinese Academy of Sciences; University of Michigan System; University of Michigan
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0345
• 发表日期: 2025
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; solvability; consumption; uniqueness; MARKETS; BSDEs

摘要

This paper addresses the portfolio selection problem for nonlinear law-dependent preferences in continuous time, which inherently exhibit time inconsistency. Employing the method of the stochastic maximum principle, we establish verification theorems for equilibrium strategies, accommodating both random market coefficients and incomplete markets. We derive the first-order condition (FOC) for the equilibrium strategies, using a notion of functional derivatives with respect to probability distributions. Then, with the help of the FOC, we obtain the equilibrium strategies in closed form for two classes of implicitly defined preferences: constant relative risk aversion and constant absolute risk aversion betweenness preferences, with deterministic market coefficients. Finally, to show applications of our theoretical results to problems with random market coefficients, we examine the weighted utility. We reveal that the equilibrium strategy can be described by a coupled system of quadratic backward stochastic differential equations. The well-posedness of this system is generally open but is established under the special structures of our problem.