{"id":4154,"date":"2017-11-04T13:39:59","date_gmt":"2017-11-04T13:39:59","guid":{"rendered":"https:\/\/detralytics.com\/?p=4154"},"modified":"2026-08-21T13:31:46","modified_gmt":"2026-08-21T13:31:46","slug":"quand-vilfredo-pareto-rencontre-jeanne-calment","status":"publish","type":"post","link":"https:\/\/detralytics.com\/fr\/publication\/quand-vilfredo-pareto-rencontre-jeanne-calment\/","title":{"rendered":"Quand Vilfredo Pareto rencontre Jeanne Calment&#8230;"},"content":{"rendered":"<div data-elementor-type=\"wp-post\" data-elementor-id=\"4154\" class=\"elementor elementor-4154\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2480b55 e-flex e-con-boxed e-con e-parent\" data-id=\"2480b55\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;shape_divider_bottom&quot;:&quot;tilt&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-shape elementor-shape-bottom\" aria-hidden=\"true\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewbox=\"0 0 1000 100\" preserveaspectratio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M0,6V0h1000v100L0,6z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-16ab746 elementor-widget elementor-widget-heading\" data-id=\"16ab746\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Quand Vilfredo Pareto rencontre Jeanne Calment\u2026<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-19508a5 elementor-widget elementor-widget-heading\" data-id=\"19508a5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">DetraNote 2017-1<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-87f3931 e-flex e-con-boxed e-con e-parent\" data-id=\"87f3931\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-9aa7e1d e-con-full e-flex e-con e-child\" data-id=\"9aa7e1d\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-67f934f elementor-widget elementor-widget-image\" data-id=\"67f934f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/detralytics.com\/wp-content\/uploads\/2017\/11\/Detra-Note-2017-01-Extreme-Mortality_Gbari_Trufin_Denuit_Detralytics.pdf\" target=\"_blank\">\n\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"768\" height=\"1092\" src=\"https:\/\/detralytics.com\/wp-content\/uploads\/2017\/11\/Miniature-Quand-Vilfredo-pareto-rencontre-jeanne-calment-768x1092.png\" class=\"elementor-animation-grow attachment-medium_large size-medium_large wp-image-4162\" alt=\"Quand Vilfredo pareto rencontre jeanne calment- Detralytics\" srcset=\"https:\/\/detralytics.com\/wp-content\/uploads\/2017\/11\/Miniature-Quand-Vilfredo-pareto-rencontre-jeanne-calment-768x1092.png 768w, https:\/\/detralytics.com\/wp-content\/uploads\/2017\/11\/Miniature-Quand-Vilfredo-pareto-rencontre-jeanne-calment-760x1080.png 760w, https:\/\/detralytics.com\/wp-content\/uploads\/2017\/11\/Miniature-Quand-Vilfredo-pareto-rencontre-jeanne-calment.png 954w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-420ffe4 elementor-align-center elementor-widget elementor-widget-button\" data-id=\"420ffe4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/detralytics.com\/wp-content\/uploads\/2017\/11\/Detra-Note-2017-01-Extreme-Mortality_Gbari_Trufin_Denuit_Detralytics.pdf\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-icon\">\n\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-far-arrow-alt-circle-down\" viewbox=\"0 0 512 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M256 8C119 8 8 119 8 256s111 248 248 248 248-111 248-248S393 8 256 8zm0 448c-110.5 0-200-89.5-200-200S145.5 56 256 56s200 89.5 200 200-89.5 200-200 200zm-32-316v116h-67c-10.7 0-16 12.9-8.5 20.5l99 99c4.7 4.7 12.3 4.7 17 0l99-99c7.6-7.6 2.2-20.5-8.5-20.5h-67V140c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12z\"><\/path><\/svg>\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">T\u00e9l\u00e9charger<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2e62cc6 e-con-full e-flex e-con e-child\" data-id=\"2e62cc6\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-fc5d00b elementor-widget elementor-widget-heading\" data-id=\"fc5d00b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Introduction<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f1e1dc7 elementor-widget elementor-widget-text-editor\" data-id=\"f1e1dc7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Les tables XR (pour les op\u00e9rations en cas de vie) et XK (pour les op\u00e9rations en cas de d\u00e9c\u00e8s) ont d\u00e9sormais remplac\u00e9 les anciennes tables r\u00e8glementaires MR\/FR et MK\/FK. Le positionnement de la mortalit\u00e9 d\u2019un portefeuille par rapport \u00e0 ces tables est le plus souvent fiable pour les assur\u00e9s relativement jeunes en raison de l\u2019abondance des donn\u00e9es disponibles sur cette tranche d\u2019\u00e2ges. Aux \u00e2ges tr\u00e8s avanc\u00e9s (au-del\u00e0 de 90 ou 100 ans, disons), le probl\u00e8me est plus difficile \u00e0 r\u00e9soudre car les effectifs en portefeuille deviennent g\u00e9n\u00e9ralement tr\u00e8s faibles. La pr\u00e9sente note \u00e9tudie pr\u00e9cis\u00e9ment la mortalit\u00e9 aux grands \u00e2ges en Belgique. Afin de garantir un volume de donn\u00e9es suffisant, nous consid\u00e8rerons la population g\u00e9n\u00e9rale belge et nous utiliserons des techniques adapt\u00e9es \u00e0 l\u2019analyse de la mortalit\u00e9 aux \u00e2ges tr\u00e8s avanc\u00e9s propos\u00e9es par Gbari, Poulain, Dal et Denuit (2017). Ceci nous am\u00e8nera \u00e0 proposer des tables d\u2019exp\u00e9rience pour la mortalit\u00e9 \u00e0 ces \u00e2ges avanc\u00e9s ainsi qu\u2019une correction de la table XR, que nous appellerons XR+, afin de tenir compte de la stabilisation des quotients de mortalit\u00e9 mise en \u00e9vidence par Rootz\u00e9n et Zholud (2017) \u00e0 l\u2019aide de l\u2019International Database on Longevity (IDL).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-0f29719 e-con-full e-flex e-con e-child\" data-id=\"0f29719\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;gradient&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2952de9 elementor-widget__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"2952de9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><b>Secteur : <\/b>Assurance<\/p><p><b><\/b><b>Expertise: <\/b>Assurance Vie<\/p><p><b>Auteurs :<\/b> Samuel Gbari,<\/p><p>Michel Denuit et<\/p><p>Julien Trufin<\/p><p><b>\u00c9diteur :<\/b> Detralytics<\/p><p><b>Date:<\/b> November 2017<\/p><p><b>Langue :<\/b> French<\/p><p><b>Pages:<\/b> 18<\/p><p><b>R\u00e9f\u00e9rence :<\/b> Detra Note 2017-1<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-c6ae38d e-flex e-con-boxed e-con e-parent\" data-id=\"c6ae38d\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a1c05c2 elementor-widget elementor-widget-spacer\" data-id=\"a1c05c2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f183faa elementor-widget elementor-widget-heading\" data-id=\"f183faa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">\u00c0 propos des auteurs<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-240e2b9 e-flex e-con-boxed e-con e-parent\" data-id=\"240e2b9\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-9809902 e-con-full e-flex e-con e-child\" data-id=\"9809902\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-cda474e elementor-widget elementor-widget-image\" data-id=\"cda474e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"500\" height=\"501\" src=\"https:\/\/detralytics.com\/wp-content\/uploads\/2020\/12\/Michel_Rond.png\" class=\"attachment-large size-large wp-image-2059\" alt=\"Michel Denuit\" srcset=\"https:\/\/detralytics.com\/wp-content\/uploads\/2020\/12\/Michel_Rond.png 500w, https:\/\/detralytics.com\/wp-content\/uploads\/2020\/12\/Michel_Rond-400x400.png 400w, https:\/\/detralytics.com\/wp-content\/uploads\/2020\/12\/Michel_Rond-150x150.png 150w, https:\/\/detralytics.com\/wp-content\/uploads\/2020\/12\/Michel_Rond-100x100.png 100w, https:\/\/detralytics.com\/wp-content\/uploads\/2020\/12\/Michel_Rond-250x250.png 250w, https:\/\/detralytics.com\/wp-content\/uploads\/2020\/12\/Michel_Rond-320x320.png 320w, https:\/\/detralytics.com\/wp-content\/uploads\/2020\/12\/Michel_Rond-146x146.png 146w, https:\/\/detralytics.com\/wp-content\/uploads\/2020\/12\/Michel_Rond-50x50.png 50w, https:\/\/detralytics.com\/wp-content\/uploads\/2020\/12\/Michel_Rond-75x75.png 75w, https:\/\/detralytics.com\/wp-content\/uploads\/2020\/12\/Michel_Rond-85x85.png 85w, https:\/\/detralytics.com\/wp-content\/uploads\/2020\/12\/Michel_Rond-80x80.png 80w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-fb8c355 e-con-full e-flex e-con e-child\" data-id=\"fb8c355\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9427d34 elementor-widget elementor-widget-heading\" data-id=\"9427d34\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Michel Denuit<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ea12a30 elementor-widget elementor-widget-text-editor\" data-id=\"ea12a30\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Michel est conseiller scientifique chez Detralytics, ainsi que professeur en sciences actuarielles \u00e0 l\u2019Universit\u00e9 catholique de Louvain. Il dispose d\u2019une exp\u00e9rience internationale en tant que professeur invit\u00e9 et a men\u00e9 de nombreux projets en collaboration avec l\u2019industrie. Chez Detralytics, Michel accompagne les jeunes talents, dispense des formations de pointe, stimule l\u2019innovation et supervise les projets de R&amp;D.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-b455dd6 e-flex e-con-boxed e-con e-parent\" data-id=\"b455dd6\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-826b55c e-con-full e-flex e-con e-child\" data-id=\"826b55c\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a4936f2 elementor-widget elementor-widget-image\" data-id=\"a4936f2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/detralytics.com\/wp-content\/uploads\/2025\/08\/Julien.png\" class=\"attachment-large size-large wp-image-5905\" alt=\"Julien\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-888af75 e-con-full e-flex e-con e-child\" data-id=\"888af75\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b42de73 elementor-widget elementor-widget-heading\" data-id=\"b42de73\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Julien Trufin<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c03f01f elementor-widget elementor-widget-text-editor\" data-id=\"c03f01f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Julien est Scientific Advisor chez Detralytics et Professeur en sciences actuarielles au sein du d\u00e9partement de math\u00e9matiques de l\u2019Universit\u00e9 Libre de Bruxelles. Il poss\u00e8de une exp\u00e9rience en tant que consultant et un solide parcours acad\u00e9mique d\u00e9velopp\u00e9 au sein d\u2019institutions de renom, dont l\u2019Universit\u00e9 Laval (Canada), l\u2019UCL et l\u2019ULB (Belgique). Chez Detralytics, Julien encadre les jeunes talents, dispense des formations de pointe, stimule l\u2019innovation et supervise les projets de R&amp;D.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d40bafd e-flex e-con-boxed e-con e-parent\" data-id=\"d40bafd\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8281458 elementor-widget elementor-widget-button\" data-id=\"8281458\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/detralytics.com\/fr\/publications\/\">\n\t\t\t\t\t\t<span 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