The study of worst-case scenarios (bounds) for a risk measure (e.g., Value-at-Risk) when the portfolio of risks is not completely specified is a central topic in the literature on robust risk measurement. I revisit some recent results and techniques that allow to cope with bounds for (Tail) Value-at-Risk when marginal distributions of the portfolio components are known but their interdependence is either unknown or only partially known. We draw a parallel with bounds for (Tail) Value-at-Risk under the sole knowledge of some of the moments of the portfolio sum. In the final part of the talk I will discuss the problem of deriving upper bounds for distortion risk measures on moment spaces. Explicit solutions for various set-ups of interest will be provided and discussed.
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