Faugeras, Olivier Paul and Pages, Gilles (2021) Risk Quantization by Magnitude and Propensity. TSE Working Paper, n. 21-1226, Toulouse

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Abstract

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.

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• Risk Quantization by Magnitude and Propensity. (deposited 15 Jun 2021 14:45) [Currently Displayed]
  • Risk quantization by magnitude and propensity. (deposited 07 Mar 2024 13:21)