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An analytic solution for multi-period uncertain portfolio selection problem

Author

Listed:
  • Bo Li

    (Nanjing University of Finance and Economics)

  • Yufei Sun

    (Curtin University
    Chongqing Normal University)

  • Kok Lay Teo

    (Sunway University
    Tianjin University of Finance and Economics)

Abstract

The return rates of risky assets in financial markets are usually assumed as random variables or fuzzy variables. For the ever-changing real asset market, this assumption may not always be satisfactory. Thus, it is sometimes more realistic to take the return rates as uncertain variables. However, for the existing works on multi-period uncertain portfolio selection problems, they do not find analytic optimal solutions. In this paper, we propose a method for deriving an analytic optimal solution to a multi-period uncertain portfolio selection problem. First, a new uncertain risk measure is defined to model the investment risk. Then, we formulate a bi-criteria optimization model, where the investment return is maximized, while the investment risk is minimized. On this basis, an equivalent transformation is presented to convert the uncertain bi-criteria optimization problem into an equivalent bi-criteria optimization problem. Then, by applying dynamic programming method, an analytic optimal solution is obtained. Finally, a numerical simulation is carried out to show that the proposed model is realistic and the method being developed is applicable and effective.

Suggested Citation

  • Bo Li & Yufei Sun & Kok Lay Teo, 2022. "An analytic solution for multi-period uncertain portfolio selection problem," Fuzzy Optimization and Decision Making, Springer, vol. 21(2), pages 319-333, June.
  • Handle: RePEc:spr:fuzodm:v:21:y:2022:i:2:d:10.1007_s10700-021-09367-8
    DOI: 10.1007/s10700-021-09367-8
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    References listed on IDEAS

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    3. Li, Xiang & Qin, Zhongfeng & Kar, Samarjit, 2010. "Mean-variance-skewness model for portfolio selection with fuzzy returns," European Journal of Operational Research, Elsevier, vol. 202(1), pages 239-247, April.
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