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The Wasserstein Metric and Robustness in Risk Management

Author

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  • Rüdiger Kiesel

    (Chair for Energy Trading and Finance, University of Duisburg-Essen, Campus Essen, Universitätsstraße 12, Essen 45141, Germany)

  • Robin Rühlicke

    (Chair for Energy Trading and Finance, University of Duisburg-Essen, Campus Essen, Universitätsstraße 12, Essen 45141, Germany)

  • Gerhard Stahl

    (Group Risk Management, Talanx AG, Riethorst 2, Hannover 30659, Germany)

  • Jinsong Zheng

    (Group Risk Management, Talanx AG, Riethorst 2, Hannover 30659, Germany)

Abstract

In the aftermath of the financial crisis, it was realized that the mathematical models used for the valuation of financial instruments and the quantification of risk inherent in portfolios consisting of these financial instruments exhibit a substantial model risk. Consequently, regulators and other stakeholders have started to require that the internal models used by financial institutions are robust. We present an approach to consistently incorporate the robustness requirements into the quantitative risk management process of a financial institution, with a special focus on insurance. We advocate the Wasserstein metric as the canonical metric for approximations in robust risk management and present supporting arguments. Representing risk measures as statistical functionals, we relate risk measures with the concept of robustness and hence continuity with respect to the Wasserstein metric. This allows us to use results from robust statistics concerning continuity and differentiability of functionals. Finally, we illustrate our approach via practical applications.

Suggested Citation

  • Rüdiger Kiesel & Robin Rühlicke & Gerhard Stahl & Jinsong Zheng, 2016. "The Wasserstein Metric and Robustness in Risk Management," Risks, MDPI, vol. 4(3), pages 1-14, August.
    • Handle: RePEc:gam:jrisks:v:4:y:2016:i:3:p:32-:d:77044
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    References listed on IDEAS

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    Cited by:

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    2. Birghila, Corina & Pflug, Georg Ch., 2019. "Optimal XL-insurance under Wasserstein-type ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 30-43.
    3. Cosma, Simona & Rimo, Giuseppe & Torluccio, Giuseppe, 2023. "Knowledge mapping of model risk in banking," International Review of Financial Analysis, Elsevier, vol. 89(C).
    4. M. Andrea Arias-Serna & Jean-Michel Loubes & Francisco J. Caro-Lopera, 2020. "Risk Measures Estimation Under Wasserstein Barycenter," Papers 2008.05824, arXiv.org.
    5. Patrick Kern & Axel Simroth & Henryk Zähle, 2020. "First-order sensitivity of the optimal value in a Markov decision model with respect to deviations in the transition probability function," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 165-197, August.
    6. Jan Obloj & Johannes Wiesel, 2018. "Robust estimation of superhedging prices," Papers 1807.04211, arXiv.org, revised Apr 2020.
    7. Tobias Fissler & Hajo Holzmann, 2022. "Measurability of functionals and of ideal point forecasts," Papers 2203.08635, arXiv.org.
    8. Marcelo Brutti Righi & Marlon Ruoso Moresco, 2024. "Inf-convolution and optimal risk sharing with countable sets of risk measures," Annals of Operations Research, Springer, vol. 336(1), pages 829-860, May.
    9. Marcelo Brutti Righi, 2018. "A theory for combinations of risk measures," Papers 1807.01977, arXiv.org, revised May 2023.
    10. Debora Daniela Escobar & Georg Ch. Pflug, 2020. "The distortion principle for insurance pricing: properties, identification and robustness," Annals of Operations Research, Springer, vol. 292(2), pages 771-794, September.
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    12. Daniela Escobar & Georg Pflug, 2018. "The distortion principle for insurance pricing: properties, identification and robustness," Papers 1809.06592, arXiv.org.

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