Risk Quantization by Magnitude and Propensity

29 Pages Posted: 28 May 2021

See all articles by Olivier Faugeras

Olivier Faugeras

Toulouse School of Economics

Gilles Pagès

Université Paris VI Pierre et Marie Curie

Date Written: May 27, 2021


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 high 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, p X) is obtained by mass transportation in Wasserstein metric of the law PX of X to a two-points {0,mX} 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 illustrate the proposed approach.

Keywords: magnitude-propensity, risk measure, mass transportation, optimal quantization

JEL Classification: C02, G22

Suggested Citation

Faugeras, Olivier and Pagès, Gilles, Risk Quantization by Magnitude and Propensity (May 27, 2021). Available at SSRN: https://ssrn.com/abstract=3854467 or http://dx.doi.org/10.2139/ssrn.3854467

Olivier Faugeras (Contact Author)

Toulouse School of Economics ( email )

1, Esplanade de l'Universite 31080 Toulouse Cedex
Bureau T106. 310
Toulouse, 31080

Gilles Pagès

Université Paris VI Pierre et Marie Curie ( email )

175 Rue du Chevaleret
Paris, 75013

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