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Symmetry
Volume 17
Issue 6
10.3390/sym17060959
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Article

Symmetric Adjustable Tail-Risk Measure for Distributionally Robust Optimization in Portfolio Allocation

by
Haonan Wang
,
Yunxiao Zhao
,
Yixin Guo
,
Changhe Liu
* and
Xinlin Zhang
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China
*
Author to whom correspondence should be addressed.
Symmetry 2025, 17(6), 959; https://doi.org/10.3390/sym17060959
Submission received: 14 April 2025 / Revised: 29 May 2025 / Accepted: 10 June 2025 / Published: 17 June 2025
(This article belongs to the Special Issue Symmetry in Optimal Control and Applications)
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Abstract

In this study, we begin by extending the mathematical formulation of the expectile risk measure through a key modification: replacing the expectation in its defining equation with expected shortfall. This substitution leads to a revised risk measure that more precisely captures downside risk. To handle the uncertainty of the underlying distribution, we then adopt a distributionally robust optimization framework. Notably, this robust optimization problem can be reformulated as a linear programming problem, and by employing suitable approximation techniques, we derive an analytical solution. In numerical experiments, our portfolio problem exhibits superior performance when compared to several traditional and distributionally robust optimized portfolio problems.
Keywords: expectile; expected shortfall; optimization under uncertainty; duality theory expectile; expected shortfall; optimization under uncertainty; duality theory

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MDPI and ACS Style

Wang, H.; Zhao, Y.; Guo, Y.; Liu, C.; Zhang, X. Symmetric Adjustable Tail-Risk Measure for Distributionally Robust Optimization in Portfolio Allocation. Symmetry 2025, 17, 959. https://doi.org/10.3390/sym17060959

AMA Style

Wang H, Zhao Y, Guo Y, Liu C, Zhang X. Symmetric Adjustable Tail-Risk Measure for Distributionally Robust Optimization in Portfolio Allocation. Symmetry. 2025; 17(6):959. https://doi.org/10.3390/sym17060959

Chicago/Turabian Style

Wang, Haonan, Yunxiao Zhao, Yixin Guo, Changhe Liu, and Xinlin Zhang. 2025. "Symmetric Adjustable Tail-Risk Measure for Distributionally Robust Optimization in Portfolio Allocation" Symmetry 17, no. 6: 959. https://doi.org/10.3390/sym17060959

APA Style

Wang, H., Zhao, Y., Guo, Y., Liu, C., & Zhang, X. (2025). Symmetric Adjustable Tail-Risk Measure for Distributionally Robust Optimization in Portfolio Allocation. Symmetry, 17(6), 959. https://doi.org/10.3390/sym17060959

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