Mean-variance portfolio selection with non-negative state-dependent risk aversion

Tianxiao Wang, Zhuo Jin, Jiaqin Wei*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this paper, we study the open-loop equilibrium strategy for mean-variance portfolio selection problem under the assumption that the risk tolerance of the investor is a non-negative and non-linear function of his/her wealth. We derive a sufficient and necessary condition for the existence and uniqueness of an open-loop equilibrium strategy via a coupled forward-backward stochastic differential equation. To the best of our knowledge, such an equation appears for the first time in the literature. The well-posedness of this equation is established by merely imposing Lipschitz condition on the risk tolerance. We also present two examples with non-monotone risk tolerances, where some interesting findings are revealed and the equilibrium strategies are obtained explicitly and numerically.

Original languageEnglish
Pages (from-to)657-671
Number of pages15
JournalQuantitative Finance
Issue number4
Publication statusPublished - 3 Apr 2021
Externally publishedYes


  • Equilibrium strategy
  • Forward-backward stochastic differential equation
  • Mean-variance
  • State-dependent risk aversion
  • Time-inconsistency


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