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Robust Distortion Risk Measures

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  • Carole Bernard
  • Silvana M. Pesenti
  • Steven Vanduffel

Abstract

The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well-informed decisions. In this paper, we quantify, for the class of distortion risk measures with an absolutely continuous distortion function, its robustness to distributional uncertainty by deriving its largest (smallest) value when the underlying loss distribution has a known mean and variance and, furthermore, lies within a ball - specified through the Wasserstein distance - around a reference distribution. We employ the technique of isotonic projections to provide for these distortion risk measures a complete characterisation of sharp bounds on their value, and we obtain quasi-explicit bounds in the case of Value-at-Risk and Range-Value-at-Risk. We extend our results to account for uncertainty in the first two moments and provide applications to portfolio optimisation and to model risk assessment.

Suggested Citation

  • Carole Bernard & Silvana M. Pesenti & Steven Vanduffel, 2022. "Robust Distortion Risk Measures," Papers 2205.08850, arXiv.org, revised Mar 2023.
    • Handle: RePEc:arx:papers:2205.08850
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    References listed on IDEAS

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    Cited by:

    1. Ariel Neufeld & Matthew Ng Cheng En & Ying Zhang, 2024. "Robust SGLD algorithm for solving non-convex distributionally robust optimisation problems," Papers 2403.09532, arXiv.org.
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    3. Silvana M. Pesenti & Steven Vanduffel, 2023. "Optimal Transport Divergences induced by Scoring Functions," Papers 2311.12183, arXiv.org, revised Apr 2024.

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