Risk Quantization by Magnitude and Propensity

Olivier Faugeras and Gilles Pages

No 21-1226, TSE Working Papers from Toulouse School of Economics (TSE)

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 high are the losses incurred, whereas the probabilities P (X = x) reveal how often one has to expect to su˙er 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 CVaR, which typ-ically conflate both e˙ects. In its simplest form, (mX , pX ) is obtained by mass transportation in Wasserstein metric of the law 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 usefulness of the proposed approach. Some variants, extensions and applications are also considered.

Date: 2021-06-11, Revised 2022-08
New Economics Papers: this item is included in nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.tse-fr.eu/sites/default/files/TSE/docu ... 2021/wp_tse_1226.pdf Full Text (application/pdf)
https://www.tse-fr.eu/sites/default/files/TSE/docu ... mentary_material.pdf Annexe (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tse:wpaper:125748

Access Statistics for this paper

More papers in TSE Working Papers from Toulouse School of Economics (TSE) Contact information at EDIRC.
Bibliographic data for series maintained by ().