Robust Portfolio Selection with Distributional Uncertainty and Integer Constraints

doi:10.1007/s40305-023-00466-4

Journal of the Operations Research Society of China ›› 2025, Vol. 13 ›› Issue (1): 56-82.doi: 10.1007/s40305-023-00466-4

收稿日期:2022-03-16 修回日期:2022-10-12 出版日期:2025-03-30 发布日期:2025-03-20
通讯作者: Shao-Jian Qu,Ri-Peng Huang,Ze-Shui Xu,Xiao-Guang Yang,Mark Goh E-mail:qushaojian@nuist.edu.cn;hrpeng@chzu.edu.cn;xuzeshui@263.net;xgyang@iss.ac.cn;bizgohkh@nus.edu.sg
基金资助:
This research was supported by the National Natural Science Foundation of China (Nos.72171149 and 72171123l), Natural Science Research of the Academic School of Anhui Province (No. KJ2020A0712), and Social Science Research of the Academic School of Anhui Province (No. SK2021A0683). Meanwhile, this research was also supported by Initial Scientific Research Fund of Chuzhou University (No. 2020qd39).

Robust Portfolio Selection with Distributional Uncertainty and Integer Constraints

Ri-Peng Huang¹, Ze-Shui Xu², Shao-Jian Qu³, Xiao-Guang Yang⁴, Mark Goh⁵

1 School of Mathematics and Finance, Chuzhou University, Chuzhou 239000, Anhui, China;
2 Business School, Sichuan University, Chengdu 610064, Sichuan, China;
3 School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
4 Academy of Mathematics and Systems Science CAS, Beijing 100190, China;
5 NUS Business School and the Logistics Institute-Asia Pacific, National University of Singapore, Singapore 119077, Singapore

Received:2022-03-16 Revised:2022-10-12 Online:2025-03-30 Published:2025-03-20
Contact: Shao-Jian Qu,Ri-Peng Huang,Ze-Shui Xu,Xiao-Guang Yang,Mark Goh E-mail:qushaojian@nuist.edu.cn;hrpeng@chzu.edu.cn;xuzeshui@263.net;xgyang@iss.ac.cn;bizgohkh@nus.edu.sg

摘要/Abstract

Abstract: This paper studies a robust portfolio selection problem with distributional ambiguity and integer constraint. Different from the assumption that the expected returns of risky assets are known, we define an ambiguity set containing the true probability distribution based on Kullback-Leibler (KL) divergence. In contrast to the traditional portfolio optimization model, the invested amounts of risky assets are integers, which is more in line with the real trading scenario. For tractability, we transform the resulting semiinfinite programming into a convex mixed-integer nonlinear programming (MINLP) problem by using Fenchel duality. To solve the convex MINLP problem efficiently, a modified generalized Benders decomposition (GBD) method is proposed. Through the back-test of real market data, the performance of the proposed model is not sensitive to the input parameters. Therefore, the proposed method has much importance value for both individual and institutional investors.

Key words: Kullback–Leibler divergence, Portfolio selection, Distributional uncertainty, Decomposition method

中图分类号:

90C15
90G10

. [J]. Journal of the Operations Research Society of China, 2025, 13(1): 56-82.

Ri-Peng Huang, Ze-Shui Xu, Shao-Jian Qu, Xiao-Guang Yang, Mark Goh. Robust Portfolio Selection with Distributional Uncertainty and Integer Constraints[J]. Journal of the Operations Research Society of China, 2025, 13(1): 56-82.

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