Robustness in the Optimization of Risk Measures
29 Pages Posted: 16 Oct 2018
Date Written: September 24, 2018
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
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