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Global Optimization for the Portfolio Selection Model with High-Order Moments

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Abstract

In this paper, we study the global optimality of polynomial portfolio optimization (PPO). The PPO is a kind of portfolio selection model with high-order moments and flexible risk preference parameters. We introduce a perturbation sample average approximation method, which can give a robust approximation of the PPO in form of linear conic optimization. The approximated problem can be solved globally with Moment-SOS relaxations. We summarize a semidefinite algorithm, which can be used to find reliable approximations of the optimal value and optimizer set of the PPO. Numerical examples are given to show the efficiency of the algorithm.

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Acknowledgements

The authors are grateful to the editor and the reviewers for their helpful comments and suggestions, which have improved the presentation of the paper.

Author information

Authors and Affiliations

  1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, 411105, Hunan, China

    Liu Yang

  2. School of Mathematics and Computational Sciences, Xiangtan University, Xiangtan, 411105, Hunan, China

    Liu Yang

  3. School of Mathematics, Hunan City University, Yiyang, 413000, Hunan, China

    Yi Yang

  4. Department of Mathematics, Texas A &M University, College Station, Texas, 77843, USA

    Su-Han Zhong

Authors
  1. Liu Yang
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  2. Yi Yang
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  3. Su-Han Zhong
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Contributions

L. Yang and S.-H. Zhong wrote this paper and designed the algorithm and finished the theoretical proof. Y. Yang performed the experiments. All authors have read and approved the final manuscript.

Corresponding author

Correspondence to Liu Yang.

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Conflict of interest

The authors declare no conflict of interest. The funding sponsors had no role in the design of the study; in the collection, analysis or interpretation of data; in the writing of the manuscript; nor in the decision to publish the results.

Additional information

Liu Yang is supported by the National Natural Science Foundation of China (Nos.12071399 and 12171145), Project of Scientific Research Fund of Hunan Provincial Science and Technology Department (No.2018WK4006), Project of Hunan National Center for Applied Mathematics (No.2020ZYT003).

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Yang, L., Yang, Y. & Zhong, SH. Global Optimization for the Portfolio Selection Model with High-Order Moments. J. Oper. Res. Soc. China (2023). https://doi.org/10.1007/s40305-023-00519-8

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  • DOI: https://doi.org/10.1007/s40305-023-00519-8

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