The quantification of downside risk in terms of capital requirements is a key issue for both regulators and the financial industry. This review presents the axiomatic approach, which is based on monetary risk measures. These provide a unifying mathematical framework for the determination of...

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...