eprintid: 43621 rev_number: 17 eprint_status: archive userid: 1482 importid: 105 dir: disk0/00/04/36/21 datestamp: 2021-06-15 14:45:54 lastmod: 2024-03-08 09:13:35 status_changed: 2024-03-08 09:13:35 type: monograph metadata_visibility: show creators_name: Faugeras, Olivier Paul creators_name: Pages, Gilles creators_idrefppn: 135534518 creators_idrefppn: 030737605 creators_affiliation: Toulouse School of Economics creators_halaffid: 1002422 title: Risk Quantization by Magnitude and Propensity ispublished: pub subjects: subjects_ECO 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. date: 2021-05 date_type: published publisher: TSE Working Paper official_url: http://tse-fr.eu/pub/125748 faculty: tse divisions: tse keywords: magnitude-propensity keywords: risk measure keywords: mass transportation keywords: optimal quantization language: en has_fulltext: TRUE view_date_year: 2021 full_text_status: public monograph_type: working_paper series: TSE Working Paper volume: 21-1226 place_of_pub: Toulouse pages: 30 institution: Université Toulouse Capitole department: Toulouse School of Economics book_title: TSE Working Paper oai_identifier: oai:tse-fr.eu:125748 harvester_local_overwrite: department harvester_local_overwrite: pending harvester_local_overwrite: creators_idrefppn harvester_local_overwrite: abstract harvester_local_overwrite: institution harvester_local_overwrite: place_of_pub harvester_local_overwrite: pages harvester_local_overwrite: creators_name harvester_local_overwrite: creators_halaffid oai_lastmod: 2024-03-06T13:09:30Z oai_set: tse site: ut1 citation: Faugeras, Olivier Paul and Pages, Gilles (2021) Risk Quantization by Magnitude and Propensity. TSE Working Paper, n. 21-1226, Toulouse document_url: https://publications.ut-capitole.fr/id/eprint/43621/1/wp_tse_1226.pdf