Robust Equilibrium Strategy for Mean–Variance–Skewness Portfolio Selection Problem with Long Memory

Jian-hao Kang, Nan-jing Huang (), Ben-Zhang Yang and Zhihao Hu
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Jian-hao Kang: Southwest Jiaotong University
Nan-jing Huang: Sichuan University
Ben-Zhang Yang: China Construction Bank
Zhihao Hu: Chinese Academy of Social Science

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 6, 47 pages

Abstract: Abstract This paper considers a robust time-consistent mean–variance–skewness portfolio selection problem for an ambiguity-averse investor by taking into account wealth-dependent risk aversion, wealth-dependent skewness preference, long memory and model uncertainty. The robust equilibrium investment strategy and the corresponding equilibrium value function are characterized for such a problem by employing an extended Hamilton–Jacobi–Bellman–Isaacs (HJBI) system via a game theoretic approach. Furthermore, for a special robust time-consistent mean–variance–skewness portfolio selection problem, the robust equilibrium investment strategy and the corresponding equilibrium value function are respectively obtained in semi-closed form. Finally, some numerical experiments are provided to indicate several new findings including (i) the robust equilibrium investment strategy displays long memory; (ii) in most cases, the mean–variance–skewness investor would invest more in the risky asset than the mean–variance investor; (iii) the skewness preference has no impact on the robust equilibrium investment strategy when the risk aversion coefficient is large enough; (iv) the skewness preference could slow down the reduction of investment in the risky asset due to the ambiguity aversion.

Keywords: Time-inconsistency; Mean–variance–skewness criterion; Long memory; Model uncertainty; Wealth dependence; Robust equilibrium investment strategy; 91G80; 93E20; 60H30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02697-2

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