Robustness in the Optimization of Risk Measures

• 成果类型: Article
• 署名作者: Embrechts, Paul; Schied, Alexander; Wang, Ruodu
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Waterloo
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2021.2147
• 发表日期: 2022
• 页码: 95-110
• 关键词: robustness; Value-at-risk; expected shortfall; optimization; Financial regulation

摘要

We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk-measurement-related optimization problem is robust, which we call robustness against optimization. The new notion is studied for various classes of risk measures and expected utility and loss functions. Motivated by practical issues from financial regulation, special attention is given to the two most widely used risk measures in the industry, Value-at-Risk (VaR) and Expected Shortfall (ES). We establish that for a class of general optimization problems, VaR leads to nonrobust optimizers, whereas convex risk measures generally lead to robust ones. Our results offer extra insight 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 derived.