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Time consistent behavioral portfolio policy for dynamic mean–variance formulation

Author

Listed:
  • Xiangyu Cui

    (Shanghai University of Finance and Economics)

  • Xun Li

    (The Hong Kong Polytechnic University)

  • Duan Li

    (The Chinese University of Hong Kong)

  • Yun Shi

    (Shanghai University)

Abstract

When one considers an optimal portfolio policy under a mean-risk formulation, it is essential to correctly model investors’ risk aversion which may be time variant or even state dependent. In this paper, we propose a behavioral risk aversion model, in which risk aversion is a piecewise linear function of the current excess wealth level with a reference point at the discounted investment target (either surplus or shortage), to reflect a behavioral pattern with both house money and break-even effects. Due to the time inconsistency of the resulting multi-period mean–variance model with adaptive risk aversion, we investigate the time consistent behavioral portfolio policy by solving a nested mean–variance game formulation. We derive a semi-analytical time consistent behavioral portfolio policy which takes a piecewise linear feedback form of the current excess wealth level with respect to the discounted investment target. Finally, we extend the above results to time consistent behavioral portfolio selection for dynamic mean–variance formulation with a cone constraint.

Suggested Citation

  • Xiangyu Cui & Xun Li & Duan Li & Yun Shi, 2017. "Time consistent behavioral portfolio policy for dynamic mean–variance formulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1647-1660, December.
    • Handle: RePEc:pal:jorsoc:v:68:y:2017:i:12:d:10.1057_s41274-017-0179-6
    DOI: 10.1057/s41274-017-0179-6
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    Cited by:

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    2. 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.
    3. Xiangyu Cui & Yun Shi & Lu Xu, 2017. "Alleviating time inconsistent behaviors via a competition scheme," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(5), pages 357-372, August.
    4. Cui, Xiangyu & Gao, Jianjun & Shi, Yun & Zhu, Shushang, 2019. "Time-consistent and self-coordination strategies for multi-period mean-Conditional Value-at-Risk portfolio selection," European Journal of Operational Research, Elsevier, vol. 276(2), pages 781-789.
    5. Dong-Mei Zhu & Jia-Wen Gu & Feng-Hui Yu & Tak-Kuen Siu & Wai-Ki Ching, 2021. "Optimal pairs trading with dynamic mean-variance objective," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 145-168, August.

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