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Nash equilibrium strategy for a multi-period mean–variance portfolio selection problem with regime switching

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  • Wu, Huiling
  • Chen, Hua

Abstract

This paper additionally incorporates the random decision behaviors of the decision-maker, in addiction to the randomness in the risky assets, into the decision-making process. Our work to this point is to investigate a multi-period mean–variance portfolio optimization under the assumption that the risk aversion is changeable according to the macroeconomic market state as the returns of the risky assets do. It is well known that the Markowitz's mean–variance portfolio selection problem is time-inconsistent, especially when the risk aversion is assumed to be dynamically changeable. Within a game theoretic framework, we derived the (subgame perfect Nash) equilibrium strategy and equilibrium value function in closed-form. We identify some interesting properties of the equilibrium investment strategy, the equilibrium value function, the terminal variance and the efficient frontier under the equilibrium strategy through numerical sensitivity analysis.

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  • Wu, Huiling & Chen, Hua, 2015. "Nash equilibrium strategy for a multi-period mean–variance portfolio selection problem with regime switching," Economic Modelling, Elsevier, vol. 46(C), pages 79-90.
    • Handle: RePEc:eee:ecmode:v:46:y:2015:i:c:p:79-90
    DOI: 10.1016/j.econmod.2014.12.024
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    Cited by:

    1. Liyuan Wang & Zhiping Chen, 2019. "Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion," Mathematics, MDPI, vol. 7(1), pages 1-16, January.
    2. Bian, Lihua & Li, Zhongfei & Yao, Haixiang, 2018. "Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 78-94.
    3. Helu Xiao & Tiantian Ren & Zhongbao Zhou, 2019. "Time-Consistent Strategies for the Generalized Multiperiod Mean-Variance Portfolio Optimization Considering Benchmark Orientation," Mathematics, MDPI, vol. 7(8), pages 1-26, August.
    4. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    5. Pun, Chi Seng, 2018. "Time-consistent mean-variance portfolio selection with only risky assets," Economic Modelling, Elsevier, vol. 75(C), pages 281-292.
    6. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    7. Zhou, Zhongbao & Xiao, Helu & Yin, Jialing & Zeng, Ximei & Lin, Ling, 2016. "Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 187-202.
    8. Felix Fie{ss}inger & Mitja Stadje, 2023. "Time-Consistent Asset Allocation for Risk Measures in a L\'evy Market," Papers 2305.09471, arXiv.org, revised Oct 2024.

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