Robust Distortion Risk Measures

Robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance when making well-informed risk management decisions. In this paper, we quantify for any given distortion risk measure its robustness to distributional uncertainty by deriving its range of attainable values when the underlying loss distribution has a known mean and variance and furthermore lies within a ball - specified through the Wasserstein distance - around a reference distribution. We extend our results to account for uncertainty in the first two moments and provide an application to model risk assessment.