Risk measures under model uncertainty: a Bayesian viewpoint
Abstract
We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain minimax inequality is actually an equality. We then provide conditions under which the corresponding robust risk measures, being defined as the supremum over all risk measures induced by a set of probability measures, can be represented classically in terms of one single probability measure. We focus in particular on the mixture probability measure obtained via mixing over a set of probability measures using some prior, which represents for instance the regulator's beliefs. The classical representation in terms of the mixture probability measure can then be interpreted as a Bayesian approach to robust risk measures.
Cite
@article{arxiv.2204.07115,
title = {Risk measures under model uncertainty: a Bayesian viewpoint},
author = {Christa Cuchiero and Guido Gazzani and Irene Klein},
journal= {arXiv preprint arXiv:2204.07115},
year = {2022}
}