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Robust distortion risk measures

Author

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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 characterization 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 optimization and to model risk assessment.

Suggested Citation

  • Carole Bernard & Silvana M. Pesenti & Steven Vanduffel, 2024. "Robust distortion risk measures," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 774-818, July.
    • Handle: RePEc:bla:mathfi:v:34:y:2024:i:3:p:774-818
    DOI: 10.1111/mafi.12414
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    References listed on IDEAS

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    Citations

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    Cited by:

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    2. Marlon Moresco & M'elina Mailhot & Silvana M. Pesenti, 2023. "Uncertainty Propagation and Dynamic Robust Risk Measures," Papers 2308.12856, arXiv.org, revised Feb 2024.
    3. Mario Ghossoub & Michael B. Zhu & Wing Fung Chong, 2024. "Pareto-Optimal Peer-to-Peer Risk Sharing with Robust Distortion Risk Measures," Papers 2409.05103, arXiv.org.
    4. Baishuai Zuo & Chuancun Yin, 2024. "Worst-cases of distortion riskmetrics and weighted entropy with partial information," Papers 2405.19075, arXiv.org.
    5. Silvana M. Pesenti & Steven Vanduffel, 2023. "Optimal Transport Divergences induced by Scoring Functions," Papers 2311.12183, arXiv.org, revised Apr 2024.
    6. Mengshuo Zhao & Narayanaswamy Balakrishnan & Chuancun Yin, 2024. "Extremal cases of distortion risk measures with partial information," Papers 2404.13637, arXiv.org, revised Oct 2024.
    7. Mengshuo Zhao & Chuancun Yin, 2024. "Best- and worst-case Scenarios for GlueVaR distortion risk measure with Incomplete information," Papers 2409.19902, arXiv.org.
    8. Jun Cai & Zhanyi Jiao & Tiantian Mao, 2024. "Worst-case values of target semi-variances with applications to robust portfolio selection," Papers 2410.01732, arXiv.org, revised Oct 2024.
    9. Anthony Coache & Sebastian Jaimungal, 2024. "Robust Reinforcement Learning with Dynamic Distortion Risk Measures," Papers 2409.10096, arXiv.org.
    10. Boonen, Tim J. & Jiang, Wenjun, 2024. "Robust insurance design with distortion risk measures," European Journal of Operational Research, Elsevier, vol. 316(2), pages 694-706.
    11. Marcelo Righi, 2024. "Robust convex risk measures," Papers 2406.12999, arXiv.org, revised Oct 2024.

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