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...

This article contains various results on a class of non-monotone law-invariant risk functionals, called the signed Choquet integrals. A functional characterization via comonotonic additivity is established, along with some theoretical properties including six equivalent conditions for a signed...

Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein distributionally robust optimization (DRO), achieves this by...

Distributionally robust optimization (DRO) has arose as an important paradigm to address the issue of distributional ambiguity in decision optimization. In its standard form, DRO seeks an optimal solution against the worst-possible expected value evaluated based on a set of candidate...