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 !nancial regulation, special attention is given to the twomost widely used riskmeasures in the industry, Valueat-Risk (VaR) and Expected Shortfall (ES).We establish that for a class of general optimization problems, VaR leads to nonrobust optimizers, whereas convex riskmeasures 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 !eld of robust optimization, to which some interesting links are derived.