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Robust Portfolio Selection with Distributional Uncertainty and Integer Constraints

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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 semi-infinite 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.

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Notes

  1. https://sourceforge.net/projects/lpsolve/.

  2. Here \(\beta _{p}\) is a measure of how much systematic risk (see [60]).

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Acknowledgements

The authors are thankful to the editors and anonymous referees. Their comments and suggestions will greatly help us to improve this paper.

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Author notes

  1. 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).

Authors and Affiliations

  1. School of Mathematics and Finance, Chuzhou University, Chuzhou, 239000, Anhui, China

    Ri-Peng Huang

  2. Business School, Sichuan University, Chengdu, 610064, Sichuan, China

    Ze-Shui Xu

  3. School of Management Science and Engineering, Nan**g University of Information Science and Technology, Nan**g, 210044, Jiangsu, China

    Shao-Jian Qu

  4. Academy of Mathematics and Systems Science CAS, Bei**g, 100190, China

    **ao-Guang Yang

  5. NUS Business School and the Logistics Institute-Asia Pacific, National University of Singapore, Singapore, 119077, Singapore

    Mark Goh

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  1. Ri-Peng Huang
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Contributions

In this paper, R.-P. Huang is in charge of methodology, model, software, and writing-original draft. Z.-S. Xu is in charge of conceptualization, methodology, and formal analysis. S.-J. Qu is in charge of methodology, supervision, and project administration. X.-G. Yang is in charge of methodology and the correctness of paper writing. M. Goh is in charge of methodology and the correctness of paper writing.

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Correspondence to Shao-Jian Qu.

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Huang, RP., Xu, ZS., Qu, SJ. et al. Robust Portfolio Selection with Distributional Uncertainty and Integer Constraints. J. Oper. Res. Soc. China (2023). https://doi.org/10.1007/s40305-023-00466-4

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