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Mean-Variance Asset-Liability Management with State-Dependent Risk Aversion

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  • Qian Zhao
  • Jiaqin Wei
  • Rongming Wang

Abstract

In this paper, we consider the asset-liability management under the mean-variance criterion. The financial market consists of a risk-free bond and a stock whose price process is modeled by a geometric Brownian motion. The liability of the investor is uncontrollable and is modeled by another geometric Brownian motion. We consider a specific state-dependent risk aversion which depends on a power function of the liability. By solving a flow of FBSDEs with bivariate state process, we obtain the equilibrium strategy among all the open-loop controls for this time-inconsistent control problem. It shows that the equilibrium strategy is a feedback control of the liability.

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  • Qian Zhao & Jiaqin Wei & Rongming Wang, 2013. "Mean-Variance Asset-Liability Management with State-Dependent Risk Aversion," Papers 1304.7882, arXiv.org.
    • Handle: RePEc:arx:papers:1304.7882
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    References listed on IDEAS

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    6. Ping Chen & Hailiang Yang, 2011. "Markowitz's Mean-Variance Asset-Liability Management with Regime Switching: A Multi-Period Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(1), pages 29-50.
    7. Chen, Ping & Yang, Hailiang & Yin, George, 2008. "Markowitz's mean-variance asset-liability management with regime switching: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 456-465, December.
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