{"id":4393,"date":"2021-01-08T16:22:23","date_gmt":"2021-01-08T16:22:23","guid":{"rendered":"https:\/\/detralytics.com\/?p=4393"},"modified":"2026-06-22T14:49:11","modified_gmt":"2026-06-22T14:49:11","slug":"risk-sharing-under-the-dominant-peer-to-peer-property-and-casualty-insurance-business-models","status":"publish","type":"post","link":"https:\/\/detralytics.com\/fr\/publications\/risk-sharing-under-the-dominant-peer-to-peer-property-and-casualty-insurance-business-models\/","title":{"rendered":"Risk sharing under the dominant peer-to-peer property and casualty insurance business models"},"content":{"rendered":"<div data-elementor-type=\"wp-post\" data-elementor-id=\"4393\" class=\"elementor elementor-4393\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-058ed83 e-flex e-con-boxed e-con e-parent\" data-id=\"058ed83\" 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-1392049 elementor-widget elementor-widget-heading\" data-id=\"1392049\" 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\">Risk sharing under the dominant peer-to-peer property and casualty insurance business models<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9b19b29 elementor-widget elementor-widget-heading\" data-id=\"9b19b29\" 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 2021-2<\/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-5f9ec9e e-flex e-con-boxed e-con e-parent\" data-id=\"5f9ec9e\" 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-828d3db e-con-full e-flex e-con e-child\" data-id=\"828d3db\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4be6218 elementor-widget elementor-widget-image\" data-id=\"4be6218\" data-element_type=\"widget\" data-e-type=\"widget\" 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\/>\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-9d90035 elementor-align-center elementor-widget elementor-widget-button\" data-id=\"9d90035\" 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:\/\/dial.uclouvain.be\/pr\/boreal\/object\/boreal%3A248773\/datastream\/PDF_01\/view\" target=\"_blank\">\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 class=\"elementor-element elementor-element-3c5e27e elementor-widget elementor-widget-spacer\" data-id=\"3c5e27e\" 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>\n\t\t<div class=\"elementor-element elementor-element-6ee1595 e-con-full e-flex e-con e-child\" data-id=\"6ee1595\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8b92d3b elementor-widget elementor-widget-heading\" data-id=\"8b92d3b\" 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-fc1d9e3 elementor-widget elementor-widget-text-editor\" data-id=\"fc1d9e3\" 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<div class=\"page\" title=\"Page 3\"><div class=\"layoutArea\"><div class=\"column\"><p>This paper purposes to formalize the three business models dominating peer-to-peer (P2P) property and casualty insurance: the self-governing model, the broker model, and the carrier model. The former one develops outside the insurance market whereas the latter ones may originate from the insurance industry, by partnering with an existing company or by issuing a new generation of participating insurance policies where part of the risk is shared within a community and higher losses, exceeding the community&#8217;s risk-bearing capacity are covered by an insurance or reinsurance company. The present paper proposes an actuarial modeling based on conditional mean risk sharing, to support the development of this new P2P insurance offer under each of the three business models. In addition, several specific questions are also addressed in the self-governing model. Considering an economic agent who has to select the optimal pool for a risk to be shared with other participants, it is shown that uniform comparison of the Lorenz or concentration curves associated to the respective total losses of the pools under consideration allows the agent to decide which pool is preferable.<\/p><p><strong><span style=\"color: #097566;\">Mots-cl\u00e9s : <\/span><\/strong>Risk pooling, conditional mean risk sharing, Lorenz curve, concentration curve, convex order.<\/p><\/div><\/div><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8512dfd e-con-full e-flex e-con e-child\" data-id=\"8512dfd\" 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-d705903 elementor-widget__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"d705903\" 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>Casualty Insurance<\/p><p><b>Auteurs :<\/b> Michel Denuit and<\/p><p>Christian Y. Robert<\/p><p><b>Publication:<\/b> Risk Management and<\/p><p>Insurance Review<\/p><p><b>Date:<\/b> January 2024<\/p><p><b>Langue :<\/b> Anglais<\/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-53f26ef e-flex e-con-boxed e-con e-parent\" data-id=\"53f26ef\" 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-45ca7dd e-con-full e-flex e-con e-child\" data-id=\"45ca7dd\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d43f55d elementor-widget elementor-widget-image\" data-id=\"d43f55d\" 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-f0de6fc e-con-full e-flex e-con e-child\" data-id=\"f0de6fc\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-224cb75 elementor-widget elementor-widget-heading\" data-id=\"224cb75\" 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-58dff6d elementor-widget elementor-widget-text-editor\" data-id=\"58dff6d\" 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=\"782\" height=\"782\" src=\"https:\/\/detralytics.com\/wp-content\/uploads\/2023\/09\/Christian_rond.png\" class=\"attachment-large size-large wp-image-4257\" alt=\"\" srcset=\"https:\/\/detralytics.com\/wp-content\/uploads\/2023\/09\/Christian_rond.png 782w, https:\/\/detralytics.com\/wp-content\/uploads\/2023\/09\/Christian_rond-768x768.png 768w\" sizes=\"(max-width: 782px) 100vw, 782px\" \/>\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\">Christian Y. Robert<\/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 class=\"has-text-color has-link-color wp-elements-035ef09b0166215eefc8d715235c0abf\">Christian est Directeur de l\u2019ISFA \u00e0 Lyon (France) et Professeur en sciences actuarielles et statistiques. Il a \u00e9galement exerc\u00e9 la fonction de Directeur de la recherche du Laboratoire de Finance et de Sciences Actuarielles de l\u2019ISFA (Lyon).<\/p><p class=\"has-text-color has-link-color wp-elements-5f6029e2ba57dd290180554cbeec9039\">Membre Honoraire de l\u2019Institut des Actuaires (Paris), Christian a publi\u00e9 plus de 50 articles scientifiques.<\/p><p class=\"has-text-color has-link-color wp-elements-68b15511a4fcf8520607bb090aa70025\">Christophe de Fays est Senior Expert et Domain Lead Non-Vie R\u00e9glementaire chez Detralytics. Apr\u00e8s plusieurs ann\u00e9es dans le conseil en IT, il a d\u00e9velopp\u00e9 une solide expertise en sciences actuarielles et en gestion de projets au sein de plusieurs grandes compagnies d\u2019assurance en Belgique. Il apporte une expertise de pointe aux projets de R&amp;D et est \u00e9galement responsable de la formation continue de nos consultants chez Detralytics.<\/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-70b872c e-flex e-con-boxed e-con e-parent\" data-id=\"70b872c\" 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-81e2ac7 elementor-widget elementor-widget-button\" data-id=\"81e2ac7\" 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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