{"id":4517,"date":"2024-07-01T13:59:24","date_gmt":"2024-07-01T13:59:24","guid":{"rendered":"https:\/\/detralytics.com\/?p=4517"},"modified":"2026-08-21T13:31:10","modified_gmt":"2026-08-21T13:31:10","slug":"participating-life-insurances-in-an-equity-libor-market-model","status":"publish","type":"post","link":"https:\/\/detralytics.com\/fr\/publication\/participating-life-insurances-in-an-equity-libor-market-model\/","title":{"rendered":"Participating life insurances in an equity-libor market model"},"content":{"rendered":"<div data-elementor-type=\"wp-post\" data-elementor-id=\"4517\" class=\"elementor elementor-4517\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-afe0603 e-flex e-con-boxed e-con e-parent\" data-id=\"afe0603\" 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-738619b elementor-widget elementor-widget-heading\" data-id=\"738619b\" 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\">Participating life insurances in an equity-libor market model<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a9385a4 elementor-widget elementor-widget-heading\" data-id=\"a9385a4\" 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 2024-4<\/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\/2024\/09\/DetraNote-2024-04-ALM_participating_life_insurance.pdf\" target=\"_blank\">\n\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"767\" height=\"1080\" src=\"https:\/\/detralytics.com\/wp-content\/uploads\/2024\/07\/Miniature-Participating-life-insurances-in-an-equity-libor-market-model-767x1080.png\" class=\"elementor-animation-grow attachment-large size-large wp-image-4519\" alt=\"\" srcset=\"https:\/\/detralytics.com\/wp-content\/uploads\/2024\/07\/Miniature-Participating-life-insurances-in-an-equity-libor-market-model-767x1080.png 767w, https:\/\/detralytics.com\/wp-content\/uploads\/2024\/07\/Miniature-Participating-life-insurances-in-an-equity-libor-market-model-768x1081.png 768w, https:\/\/detralytics.com\/wp-content\/uploads\/2024\/07\/Miniature-Participating-life-insurances-in-an-equity-libor-market-model.png 1078w\" sizes=\"(max-width: 767px) 100vw, 767px\" \/>\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\/2024\/09\/DetraNote-2024-04-ALM_participating_life_insurance.pdf\" 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>\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<div class=\"page\" title=\"Page 3\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p>This article introduces an equity-Libor Market Model (LMM) that integrates the investment strategy into the valuation process of participating life insurances. Within this framework, we consider bond portfolios rebalanced across multiple maturities and provide a semi-analytical formula for approximating the fair value of liabilities. We then investigate the impact of the investment policy on the net asset value and the solvency capital requirement. To carry out this analysis, we propose a Monte Carlo method for generating sample paths under both Libor and real measures, alongside an estimation procedure under the real measure. The nu- merical illustration focuses on the asset-liability management of an endowment and a life annuity.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><strong><span style=\"color: #097566;\">Mots-cl\u00e9s : <\/span><\/strong>Libor market model, life insurance, asset-liability management<\/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>Donatien Hainaut and<\/p><div class=\"page\" title=\"Page 3\"><div class=\"layoutArea\"><div class=\"column\"><p>Laurent Devineau\u0084<\/p><\/div><\/div><\/div><p>\u00a0<\/p><p><b>\u00c9diteur :<\/b> Detralytics<\/p><p><b>Date:<\/b> July 2024<\/p><p><b>Langue :<\/b> Anglais<\/p><p><b>Pages:<\/b> 29<\/p><p><b>R\u00e9f\u00e9rence :<\/b> Detra Note 2024-4<\/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=\"800\" height=\"800\" src=\"https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond.jpg\" class=\"attachment-large size-large wp-image-2876\" alt=\"Donatien Hainaut\" srcset=\"https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond.jpg 1042w, https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond-768x768.jpg 768w, https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond-146x146.jpg 146w, https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond-50x50.jpg 50w, https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond-75x75.jpg 75w, https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond-85x85.jpg 85w, https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond-80x80.jpg 80w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\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\">Donatien Hainaut<\/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 class=\"has-text-color has-link-color wp-elements-ae5c48d82f22f2e0c01ebb851eee595b\">Donatien Hainaut est Conseiller Scientifique chez Detralytics et Professeur \u00e0 l\u2019UCLouvain (Belgique), o\u00f9 il dirige le Master en Data Science \u00e0 orientation statistique. Auparavant, il a occup\u00e9 plusieurs postes acad\u00e9miques, notamment en tant que Professeur Associ\u00e9 \u00e0 la Rennes School of Business et \u00e0 l\u2019ENSAE \u00e0 Paris. Il poss\u00e8de \u00e9galement une solide exp\u00e9rience en entreprise, ayant travaill\u00e9 comme Risk Officer, Quantitative Analyst et ALM Officer.<\/p><p class=\"has-text-color has-link-color wp-elements-319687f5e483df5041193c0b748e25dd\">Actuaire qualifi\u00e9 et titulaire d\u2019un doctorat en Asset and Liability Management, ses recherches actuelles portent sur les m\u00e9canismes de contagion dans les processus stochastiques ainsi que sur les applications des r\u00e9seaux de neurones en assurance.<\/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-14cd238 elementor-widget elementor-widget-image\" data-id=\"14cd238\" 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\/2024\/07\/Laurent.png\" class=\"attachment-large size-large wp-image-7803\" alt=\"\" srcset=\"https:\/\/detralytics.com\/wp-content\/uploads\/2024\/07\/Laurent.png 500w, https:\/\/detralytics.com\/wp-content\/uploads\/2024\/07\/Laurent-12x12.png 12w\" 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-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\">Laurent Devineau<\/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\" style=\"color: #383838;\">Laurent joined Detralytics as Innovation Lead to promote innovation at the heart of the firm&#8217;s practices and strategy. A few months later, Laurent was appointed CEO of Detralytics France.<\/p><p class=\"has-text-color has-link-color\" style=\"color: #383838;\">He began his career as a teacher before joining Suravenir, where he worked on issues relating to the valuation of loan portfolios and the construction of experience laws.<\/p><p class=\"has-text-color has-link-color wp-elements-ae5c48d82f22f2e0c01ebb851eee595b\">     <\/p><p class=\"has-text-color has-link-color\" style=\"color: #383838;\">Laurent then spent nearly fifteen years managing the Research &amp; Development and Innovation activities of Milliman and Addactis. Laurent was also Head of Risk Measurement at Allianz France, where he was responsible for calculating the entity&#8217;s Solvency 2 economic capital.<\/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-e27d120 e-flex e-con-boxed e-con e-parent\" data-id=\"e27d120\" 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-a29f0c6 elementor-widget elementor-widget-button\" data-id=\"a29f0c6\" 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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<\/p>","protected":false},"author":1,"featured_media":4519,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[133],"tags":[],"class_list":["post-4517","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-publication"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Detra Note : life insurances in an equity-libor market model<\/title>\n<meta name=\"description\" content=\"This article introduces an equity-Libor Market Model (LMM) that integrates the investment strategy into the valuation process of participating life insurances.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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