Robustness in the Optimization of Risk Measures

We study issues of robustness in the context Quantitative Risk Management and Optimization. develop a general methodology for determining whether given risk-measurement-related optimization problem is robust, which we call “robustness against optimization.” The new notion studied various classes risk measures expected utility loss functions. Motivated by practical from !nancial regulation, special attention to twomost widely used riskmeasures industry, Valueat-Risk (VaR) Expected Shortfall (ES).We establish that class problems, VaR leads nonrobust optimizers, whereas convex generally lead robust ones. Our results offer extra insight on ongoing discussion about comparative advantages ES banking insurance regulation. conceptually different !eld optimization, some interesting links are derived.