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

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  • Tianxiao Wang
  • Zhuo Jin
  • Jiaqin Wei

Abstract

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.

Suggested Citation

  • Tianxiao Wang & Zhuo Jin & Jiaqin Wei, 2021. "Mean-variance portfolio selection with non-negative state-dependent risk aversion," Quantitative Finance, Taylor & Francis Journals, vol. 21(4), pages 657-671, April.
    • Handle: RePEc:taf:quantf:v:21:y:2021:i:4:p:657-671
    DOI: 10.1080/14697688.2020.1787492
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