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Pré-Publication, Document De Travail Année : 2021

Risk Quantization by Magnitude and Propensity

Olivier P. Faugeras
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Résumé

We propose a novel approach in the assessment of a random risk variable $X$ by introducing magnitude-propensity risk measures $(m_X,p_X)$. 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 $m_X$ and the propensity $p_X$ 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, $(m_X,p_X)$ is obtained by mass transportation in Wasserstein metric of the law $P^X$ of $X$ to a two-points $\{0, m_X\}$ discrete distribution with mass $p_X$ at $m_X$. 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.
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Dates et versions

hal-03233068 , version 1 (23-05-2021)
hal-03233068 , version 2 (25-11-2023)

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  • HAL Id : hal-03233068 , version 1

Citer

Olivier P. Faugeras, Gilles Pages. Risk Quantization by Magnitude and Propensity. 2021. ⟨hal-03233068v1⟩
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