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Time-Consistent Portfolio Policy for Asset-Liability Mean-Variance Model with State-Dependent Risk Aversion

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Abstract

In reality, when facing a multi-period asset-liability portfolio selection problem, the risk aversion attitude of a mean-variance investor may depend on the wealth level and liability level. Thus, in this paper, we propose a state-dependent risk aversion model for the investor, in which risk aversion is a linear function of current wealth level and current liability level. Due to the time inconsistency of the resulting multi-period asset-liability mean-variance model, we investigate its time-consistent portfolio policy by solving a nested mean-variance game formulation. We derive the analytical time-consistent portfolio policy, which takes a linear form of current wealth level and current liability level. We also analyze the influence of the risk aversion coefficients on the time-consistent portfolio policy and the investment performance via a numerical example.

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Authors and Affiliations

  1. School of Management, Shanghai University, Shanghai, 200444, China

    Liu-Meng Peng & Yun Shi

  2. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, 200433, China

    Xiang-Yu Cui

Authors
  1. Liu-Meng Peng
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  2. Xiang-Yu Cui
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  3. Yun Shi
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Corresponding author

Correspondence to Yun Shi.

Additional information

This paper is dedicated to Professor Duan Li in celebration of his 65th birthday.

This research was supported by the National Natural Science Foundation of China (Nos. 71601107, 71671106 and 71201094), Shanghai Pujiang Program (No. 15PJC051), the State Key Program in the Major Research Plan of National Natural Science Foundation of China (No. 91546202) and Program for Innovative Research Team of Shanghai University of Finance and Economics.

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Peng, LM., Cui, XY. & Shi, Y. Time-Consistent Portfolio Policy for Asset-Liability Mean-Variance Model with State-Dependent Risk Aversion. J. Oper. Res. Soc. China 6, 175–188 (2018). https://doi.org/10.1007/s40305-018-0191-9

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  • DOI: https://doi.org/10.1007/s40305-018-0191-9

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