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The Wasserstein Metric and Robustness in Risk Management

Chair for Energy Trading and Finance, University of Duisburg-Essen, Campus Essen, Universitätsstraße 12, Essen 45141, Germany
Group Risk Management, Talanx AG, Riethorst 2, Hannover 30659, Germany
Author to whom correspondence should be addressed.
Academic Editor: Mogens Steffensen
Risks 2016, 4(3), 32;
Received: 13 May 2016 / Revised: 5 August 2016 / Accepted: 15 August 2016 / Published: 31 August 2016
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. View Full-Text
Keywords: risk management; Wasserstein metric; robustness; risk measures risk management; Wasserstein metric; robustness; risk measures
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Kiesel, R.; Rühlicke, R.; Stahl, G.; Zheng, J. The Wasserstein Metric and Robustness in Risk Management. Risks 2016, 4, 32.

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