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

doi:10.1007/s40305-023-00519-8

Journal of the Operations Research Society of China ›› 2025, Vol. 13 ›› Issue (4): 1226-1247.doi: 10.1007/s40305-023-00519-8

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

Liu Yang^1,2, Yi Yang³, Su-Han Zhong⁴

1 Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, Hunan, China;
2 School of Mathematics and Computational Sciences, Xiangtan University, Xiangtan 411105, Hunan, China;
3 School of Mathematics, Hunan City University, Yiyang 413000, Hunan, China;
4 Department of Mathematics, Texas A&M University, College Station, Texas 77843, USA

Received:2022-12-24 Revised:2023-09-08 Online:2025-12-30 Published:2025-12-19
Contact: Liu Yang E-mail:yangl410@xtu.edu.cn
Supported by:
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).

Abstract

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.

Key words: Portfolio selection model, High-order moments, Moment-SOS relaxation, Perturbation sample average approximation

CLC Number:

Liu Yang, Yi Yang, Su-Han Zhong. Global Optimization for the Portfolio Selection Model with High-Order Moments[J]. Journal of the Operations Research Society of China, 2025, 13(4): 1226-1247.

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

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