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Generalized expected-shortfalls based on distortion risk measures

Author

Listed:
  • Gong, Shuyu
  • Zou, Zhenfeng
  • Guan, Meng
  • Hu, Taizhong

Abstract

This paper establishes explicit representations of generalized Expected-Shortfall (ES) based on a distortion risk measure with arbitrary (possibly non-differentiable) distortion function. We further derive a novel reverse generalized-ES optimization formula, which enables one to obtain closed-form solutions for the supremum value of a stop-loss random variable’s distortion risk measure over a Wasserstein-2 uncertainty set constrained by the first two moments, and exact characterization of the extremal distribution attaining this bound. The method is validated through an insurance data case study, demonstrating its applicability in risk management scenarios with distributional ambiguity.

Suggested Citation

  • Gong, Shuyu & Zou, Zhenfeng & Guan, Meng & Hu, Taizhong, 2026. "Generalized expected-shortfalls based on distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 127(C).
    • Handle: RePEc:eee:insuma:v:127:y:2026:i:c:s0167668725001520
    DOI: 10.1016/j.insmatheco.2025.103206
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    Keywords

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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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