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Robust distortion risk measures with linear penalty under distribution uncertainty

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  • Yuxin Du
  • Dejian Tian
  • Hui Zhang

Abstract

The paper investigates the robust distortion risk measure with linear penalty function under distribution uncertainty. The distribution uncertainties are characterized by predetermined moment conditions or constraints on the Wasserstein distance. The optimal quantile distribution and the optimal value function are explicitly characterized. Our results partially extend the results of Bernard, Pesenti and Vanduffel (2024) and Li (2018) to robust distortion risk measures with linear penalty. In addition, we also discuss the influence of the penalty parameter on the optimal solution.

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  • Yuxin Du & Dejian Tian & Hui Zhang, 2025. "Robust distortion risk measures with linear penalty under distribution uncertainty," Papers 2503.15824, arXiv.org.
    • Handle: RePEc:arx:papers:2503.15824
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    File URL: http://arxiv.org/pdf/2503.15824
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