Actuarial Science Seminar: Risk Assessment under Uncertainty

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 will first discuss 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. Next, I discuss upper bounds for distortion risk measures when only the mean and some other higher order moment (such as the variance) of the portfolio loss is known, possibly supplemented with structural information such as unimodality and non-negativity of the portfolio loss.