Seminar A general Wasserstein-type distance and stability of law-invariant risk measures

Abstract

We introduce and study the properties of a Wasserstein-type distance between Borel laws on Polish spaces. The construction is fairly general, going well beyond the L^p case. We then apply the distance in a natural way for assessing stability properties of law-invariant convex risk measures defi
ned on general rearrangement-invariant spaces of random variables, including Orlicz spaces as a prominent example.
Particular focus is given to the entropic and spectral risk measures, for which explicit bounds are derived.
Finally, we prove stability of an Optimal Transport problem with entropic penalties with respect to the newly introduced distance and discuss this result within a financial perspective.

(joint work with A. Doldi)