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

Tianxiao Wang, Zhuo Jin and Jiaqin Wei

Quantitative Finance, 2021, vol. 21, issue 4, 657-671

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.

Date: 2021
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DOI: 10.1080/14697688.2020.1787492

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