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Dynamic portfolio selection for nonlinear law-dependent preferences

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  • Zongxia Liang
  • Jianming Xia
  • Fengyi Yuan

Abstract

This paper addresses the portfolio selection problem for nonlinear law-dependent preferences in continuous time, which inherently exhibit time inconsistency. Employing the method of 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: CRRA and CARA 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 (QBSDEs). The well-posedness of this system is generally open but is established under the special structures of our problem.

Suggested Citation

  • Zongxia Liang & Jianming Xia & Fengyi Yuan, 2023. "Dynamic portfolio selection for nonlinear law-dependent preferences," Papers 2311.06745, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:2311.06745
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    References listed on IDEAS

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    Cited by:

    1. Zongxia Liang & Jianming Xia & Keyu Zhang, 2023. "Equilibrium stochastic control with implicitly defined objective functions," Papers 2312.15173, arXiv.org, revised Dec 2023.

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