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

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  • Qian Zhao
  • Jiaqin Wei
  • Rongming Wang
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    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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    File URL: http://arxiv.org/pdf/1304.7882
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    Paper provided by arXiv.org in its series Papers with number 1304.7882.

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    Date of creation: Apr 2013
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    Handle: RePEc:arx:papers:1304.7882

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    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, American Finance Association, vol. 7(1), pages 77-91, 03.
    2. 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, Taylor & Francis Journals, vol. 18(1), pages 29-50.
    3. Chiu, Mei Choi & Li, Duan, 2006. "Asset and liability management under a continuous-time mean-variance optimization framework," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 330-355, December.
    4. Markus LEIPPOLD & Fabio TROJANI & Paolo VANINI, 2002. "A Geometric Approach to Multiperiod Mean Variance Optimization of Assets and Liabilities," FAME Research Paper Series, International Center for Financial Asset Management and Engineering rp48, International Center for Financial Asset Management and Engineering.
    5. 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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