On the Geometry of Acceptability Functionals

Abstract

In this paper we discuss the geometry of acceptability functionals or risk measures. The dependenceof the random variable is investigated first. The main contribution and focus of this paper is to studyhow acceptability functionals vary whenever the underlying probability measure is perturbed. It turns out that the Wasserstein distance provides a valuable notion of distance, and may acceptability functionals allow a precise quantification in terms of this distance.