Steven Vanduffel (Vrije Universiteit Brussels, Belgium)

Title: Risk Bounds Under Uncertainty

We study for any given distortion risk measure its robustness to distributional uncertainty by deriving its largest (smallest) value when the underlying loss distribution lies within a ball – specified through the Wasserstein distance - around a reference distribution. We employ isotonic projections to provide for any distortion risk measure a complete characterization of sharp bounds. We generalize our results by deriving sharp bounds when distributional uncertainty is described via Bregman-Wasserstein balls and also deal with the case of distortion risk metrics. Applications to model risk assessment as well as to portfolio choice under ambiguity are discussed. The talk is based on joint works with Carole Bernard, Silvana Pesenti, Peng Liu and Yi Xia.