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The Wasserstein Metric and Robustness in Risk Management

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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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    1. Busse, Marc & Müller, Ulrich & Dacorogna, Michel, 2010. "Robust Estimation of Reserve Risk," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 453-489, November.
    2. Philippe Jorion, 2009. "Risk Management Lessons from the Credit Crisis," European Financial Management, European Financial Management Association, vol. 15(5), pages 923-933, November.
    3. John C. Hull, 2009. "The Credit Crunch of 2007: What Went Wrong? Why? What Lessons Can be Learned?," World Scientific Book Chapters, in: Douglas D Evanoff & Philipp Hartmann & George G Kaufman (ed.), The First Credit Market Turmoil Of The 21st Century Implications for Public Policy, chapter 11, pages 161-174, World Scientific Publishing Co. Pte. Ltd..
    4. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 593-606.
    5. Stefan Weber, 2006. "Distribution‐Invariant Risk Measures, Information, And Dynamic Consistency," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 419-441, April.
    6. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    7. Barrieu, Pauline & Scandolo, Giacomo, 2014. "Assessing financial model risk," LSE Research Online Documents on Economics 60084, London School of Economics and Political Science, LSE Library.
    8. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Post-Print hal-00413729, HAL.
    9. Pflug, Georg Ch. & Pichler, Alois & Wozabal, David, 2012. "The 1/N investment strategy is optimal under high model ambiguity," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 410-417.
    10. Rama Cont & Romain Deguest & Xuedong He, 2011. "Loss-Based Risk Measures," Papers 1110.1436, arXiv.org, revised Apr 2013.
    11. Krätschmer, Volker & Schied, Alexander & Zähle, Henryk, 2012. "Qualitative and infinitesimal robustness of tail-dependent statistical functionals," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 35-47, January.
    12. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
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    Cited by:

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    2. 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.
    3. 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.
    4. 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.
    5. Daniela Escobar & Georg Pflug, 2018. "The distortion principle for insurance pricing: properties, identification and robustness," Papers 1809.06592, arXiv.org.
    6. Asimit, Alexandru V. & Bignozzi, Valeria & Cheung, Ka Chun & Hu, Junlei & Kim, Eun-Seok, 2017. "Robust and Pareto optimality of insurance contracts," European Journal of Operational Research, Elsevier, vol. 262(2), pages 720-732.
    7. Birghila, Corina & Pflug, Georg Ch., 2019. "Optimal XL-insurance under Wasserstein-type ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 30-43.
    8. M. Andrea Arias-Serna & Jean-Michel Loubes & Francisco J. Caro-Lopera, 2020. "Risk Measures Estimation Under Wasserstein Barycenter," Papers 2008.05824, arXiv.org.
    9. Jan Obloj & Johannes Wiesel, 2018. "Robust estimation of superhedging prices," Papers 1807.04211, arXiv.org, revised Apr 2020.
    10. Tobias Fissler & Hajo Holzmann, 2022. "Measurability of functionals and of ideal point forecasts," Papers 2203.08635, arXiv.org.
    11. Marcelo Brutti Righi, 2018. "A theory for combinations of risk measures," Papers 1807.01977, arXiv.org, revised May 2023.
    12. Hamed Tabasi & Vahidreza Yousefi & Jolanta Tamošaitienė & Foroogh Ghasemi, 2019. "Estimating Conditional Value at Risk in the Tehran Stock Exchange Based on the Extreme Value Theory Using GARCH Models," Administrative Sciences, MDPI, vol. 9(2), pages 1-17, May.

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