Conceptualizing Robustness in Risk Management

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