Robust Portfolio Selection with Distributional Uncertainty and Integer Constraints

doi:10.1007/s40305-023-00466-4

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

CLC Number:

90C15
90G10

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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