We study for any given distortion risk measure its robustness to distributional uncertainty by deriving its largest (smallest) value 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 employ the technique of isotonic projections to provide for any distortion risk measure a complete characterisation of sharp bounds on its value and obtain analytic bounds in the case of Range-Value-at-Risk. We extend our results to account for uncertainty in the first two moments and provide an application to model risk assessment.

This is joint work with Carole Bernard and Silvana Pesenti.

Bio: Steven Vanduffel is a professor in Finance and Insurance at Vrije Universiteit Brussel (VUB). His research topics pertain to the fields of insurance and financial mathematics/engineering. His research has been published in journals such as Finance and Stochastics, Mathematical Finance, Journal of Mathematical Economics, Journal of Risk and Insurance, and Journal of Econometrics. He was awarded some prizes including the Robert Mehr Award (2022), the Robert C. Witt Award (2018), the Redington Prize (2015), and the SCOR-EGRIE Young Economist Best Paper Award (2011).