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Multi‐period mean variance portfolio selection under incomplete information

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  • Ling Zhang
  • Zhongfei Li
  • Yunhui Xu
  • Yongwu Li

Abstract

This paper solves an optimal portfolio selection problem in the discrete‐time setting where the states of the financial market cannot be completely observed, which breaks the common assumption that the states of the financial market are fully observable. The dynamics of the unobservable market state is formulated by a hidden Markov chain, and the return of the risky asset is modulated by the unobservable market state. Based on the observed information up to the decision moment, an investor wants to find the optimal multi‐period investment strategy to maximize the mean‐variance utility of the terminal wealth. By adopting a sufficient statistic, the portfolio optimization problem with incompletely observable information is converted into the one with completely observable information. The optimal investment strategy is derived by using the dynamic programming approach and the embedding technique, and the efficient frontier is also presented. Compared with the case when the market state can be completely observed, we find that the unobservable market state does decrease the investment value on the risky asset in average. Finally, numerical results illustrate the impact of the unobservable market state on the efficient frontier, the optimal investment strategy and the Sharpe ratio. Copyright © 2016 John Wiley & Sons, Ltd.

Suggested Citation

  • Ling Zhang & Zhongfei Li & Yunhui Xu & Yongwu Li, 2016. "Multi‐period mean variance portfolio selection under incomplete information," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(6), pages 753-774, November.
    • Handle: RePEc:wly:apsmbi:v:32:y:2016:i:6:p:753-774
    DOI: 10.1002/asmb.2191
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    Cited by:

    1. Reza Keykhaei, 2020. "Portfolio selection in a regime switching market with a bankruptcy state and an uncertain exit-time: multi-period mean–variance formulation," Operational Research, Springer, vol. 20(3), pages 1231-1254, September.
    2. Wang, Pei & Shen, Yang & Zhang, Ling & Kang, Yuxin, 2021. "Equilibrium investment strategy for a DC pension plan with learning about stock return predictability," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 384-407.
    3. Huang, Jia & Chen, Zheng, 2021. "Optimal risk asset allocation of a loss-averse bank with partial information under inflation risk," Finance Research Letters, Elsevier, vol. 38(C).
    4. 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.
    5. van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2021. "The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors," European Journal of Operational Research, Elsevier, vol. 289(2), pages 774-792.

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