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Elliptic entropy of uncertain random variables with application to portfolio selection

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Abstract

This paper investigates an elliptic entropy of uncertain random variables and its application in the area of portfolio selection. We first define the elliptic entropy to characterize the uncertainty of uncertain random variables and give some mathematical properties of the elliptic entropy. Then we derive a computational formula to calculate the elliptic entropy of function of uncertain random variables. Furthermore, we use the elliptic entropy to characterize the risk of investment and establish a mean-entropy portfolio selection model, in which the future security returns are described by uncertain random variables. Based on the chance theory, the equivalent form of the mean–entropy model is derived. To show the performance of the mean–entropy portfolio selection model, several numerical experiments are presented. We also numerically compare the mean–entropy model with the mean–variance model, the equi-weighted portfolio model, and the most diversified portfolio model by using three kinds of diversification indices. Numerical results show that the mean-entropy model outperforms the mean–variance model in selecting diversified portfolios no matter of using which diversification index.

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Acknowledgements

This work was supported by the Natural Science Foundation of Hebei Province (No. F2020202056), the Key Project of Hebei Education Department (No. ZD2020125), the National Natural Science Foundation of China (Nos. 11801108, 11701116).

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Authors and Affiliations

  1. College of Management and Economics, Tianjin University, Tianjin, 300072, China

    Lin Chen

  2. School of Economics and Management, Hebei University of Technology, Tianjin, 300401, China

    Rong Gao

  3. School of Business, East China University of Political Science and Law, Shanghai, 201620, China

    Yuxiang Bian

  4. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Huafei Di

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  1. Lin Chen
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  2. Rong Gao
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  3. Yuxiang Bian
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  4. Huafei Di
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Correspondence to Rong Gao or Huafei Di.

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Chen, L., Gao, R., Bian, Y. et al. Elliptic entropy of uncertain random variables with application to portfolio selection. Soft Comput 25, 1925–1939 (2021). https://doi.org/10.1007/s00500-020-05266-z

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