Robustness in the Optimization of Risk Measures

29 Pages Posted: 16 Oct 2018

See all articles by Paul Embrechts

Paul Embrechts

Swiss Federal Institute of Technology Zurich; Swiss Finance Institute

Alexander Schied

University of Mannheim

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: September 24, 2018

Abstract

In this paper, we study issues of robustness in the context of Quantitative Risk Management. Depending on the underlying objectives, we develop a general methodology for determining whether a given risk measurement related optimization problem is robust. Motivated by practical issues from financial regulation, we give special attention to the two most widely used risk measures in the industry, Value-at-Risk (VaR) and Expected Shortfall (ES). We discover that for many simple representative optimization problems, VaR generally leads to non-robust optimizers whereas ES generally leads to robust ones. Our results thus shed light from a new angle on the ongoing discussion about the comparative advantages of VaR and ES in banking and insurance regulation. Our notion of robustness is conceptually different from the field of robust optimization, to which some interesting links are discovered.

Keywords: robustness, Value-at-Risk, Expected Shortfall, optimization, financial regulation

JEL Classification: C61, G10

Suggested Citation

Embrechts, Paul and Schied, Alexander and Wang, Ruodu, Robustness in the Optimization of Risk Measures (September 24, 2018). Available at SSRN: https://ssrn.com/abstract=3254587 or http://dx.doi.org/10.2139/ssrn.3254587

Paul Embrechts

Swiss Federal Institute of Technology Zurich ( email )

ETH-Zentrum
CH-8092 Zurich
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Alexander Schied

University of Mannheim ( email )

Department of Mathematics
A 5, 6
Mannheim, 68131
Germany
+49-621-181-2513 (Phone)

HOME PAGE: http://www.alexschied.de/

Ruodu Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

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