%0 Report
%9 Working Paper
%A Faugeras, Olivier Paul
%A Pages, Gilles
%B TSE Working Paper
%C Toulouse
%D 2021
%F publications:43621
%I Université Toulouse Capitole
%K magnitude-propensity
%K risk measure
%K mass transportation
%K optimal quantization
%T Risk Quantization by Magnitude and Propensity
%U https://publications.ut-capitole.fr/id/eprint/43621/
%V 21-1226
%X We propose a novel approach in the assessment of a random risk variable X by introducing magnitude-propensity risk measures (mX; pX). This bivariate measure intends to account for the dual aspect of risk, where the magnitudes x of X tell how hign are the losses incurred, whereas the probabilities P(X = x) reveal how often one has to expect to suffer such losses. The basic idea is to simultaneously quantify both the severity mX and the propensity pX of the real-valued risk X. This is to be contrasted with traditional univariate risk measures, like VaR or Expected shortfall, which typically conflate both effects. In its simplest form, (mX; pX) is obtained by mass transportation in Wasserstein metric of the law PX of X to a two-points f0;mXg discrete distribution with mass pX at mX. The approach can also be formulated as a constrained optimal quantization problem. This allows for an informative comparison of risks on both the magnitude and propensity scales. Several examples illustratethe proposed approach.