Conceptualizing Robustness in Risk Management

23 Pages Posted: 24 May 2012 Last revised: 1 Oct 2015

See all articles by Ruediger Kiesel

Ruediger Kiesel

University of Duisburg-Essen - Faculty of Economic Science

Robin Rühlicke

University of Duisburg-Essen - Department of Economics and Business Administration

Gerhard Stahl

European Union - Committee of the Regions

Jinsong Zheng

Talanx AG

Date Written: May 24, 2012

Abstract

Two main areas of application of mathematics in finance are the valuation of financial instruments and the quantification of risk inherent in portfolios consisting of financial instruments. The mathematical models used in both areas were criticized in the aftermath of the financial crisis, due to the significant amount of model risk that was realized. Consequently, regulators and other stakeholders start to require that the internal models used by financial institutions are robust. In this paper, we answer the question how the robustness requirements can be consistently incorporated 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. Writing risk measures as statistical functionals, we relate them to this approximation approach. This allows us to use results from robust statistics concerning continuity and differentiability of such functionals. Finally, we combine the mathematical ingredients of the risk management process in the risk management space and illustrate our approach via a practical application.

Keywords: risk management, robustness, Wasserstein Metric, risk measures

JEL Classification: C18, G32

Suggested Citation

Kiesel, Ruediger and Rühlicke, Robin and Stahl, Gerhard and Zheng, Jinsong, Conceptualizing Robustness in Risk Management (May 24, 2012). Available at SSRN: https://ssrn.com/abstract=2065723 or http://dx.doi.org/10.2139/ssrn.2065723

Ruediger Kiesel

University of Duisburg-Essen - Faculty of Economic Science ( email )

Essen, 45117
Germany

HOME PAGE: http://www.lef.wiwi.uni-due.de/

Robin Rühlicke (Contact Author)

University of Duisburg-Essen - Department of Economics and Business Administration ( email )

Universitätsstr. 9
Essen, 45141
Germany

Gerhard Stahl

European Union - Committee of the Regions ( email )

Brussels
Belgium

Jinsong Zheng

Talanx AG ( email )

Riethorst 2
Hannover, NRW 30659
Germany

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