{"id":5293,"date":"2025-04-01T09:19:30","date_gmt":"2025-04-01T09:19:30","guid":{"rendered":"https:\/\/detralytics.com\/?p=5293"},"modified":"2026-08-21T13:31:09","modified_gmt":"2026-08-21T13:31:09","slug":"insurance-risk-classification-with-generalized-gaussian-process-regression-models","status":"publish","type":"post","link":"https:\/\/detralytics.com\/fr\/publication\/insurance-risk-classification-with-generalized-gaussian-process-regression-models\/","title":{"rendered":"Insurance risk classification with generalized gaussian process regression models"},"content":{"rendered":"<div data-elementor-type=\"wp-post\" data-elementor-id=\"5293\" class=\"elementor elementor-5293\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2170b5b e-flex e-con-boxed e-con e-parent\" data-id=\"2170b5b\" 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-0cf3472 elementor-widget elementor-widget-heading\" data-id=\"0cf3472\" 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\">Insurance risk classification with generalized gaussian process regression models<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0d88ffb elementor-widget elementor-widget-heading\" data-id=\"0d88ffb\" 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 2025-2<\/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-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\/2025\/04\/Detra-Note-2025-2.pdf\" target=\"_blank\">\n\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"428\" height=\"605\" src=\"https:\/\/detralytics.com\/wp-content\/uploads\/2025\/04\/Capture-decran-2025-04-01-a-11.09.36.png\" class=\"elementor-animation-grow attachment-large size-large wp-image-5299\" alt=\"Detra Note : Insurance risk classification with generalized gaussian process regression models.\" \/>\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\/2025\/04\/Detra-Note-2025-2.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 class=\"p1\">This paper proposes a new approach to risk classification based on Generalized Gaussian Process Regression (GGPR). The response under consideration obeys a distribution belonging to the Exponential Dispersion (ED) family. It typically corresponds to a claim count or a claim severity in the context of insurance studies. GGPR is a supervised machine learning method with Bayesian flavor. Individual random effects obeying a multivariate Normal distribution are connected with the help of their covariance matrix built from a so-called kernel function. The latter enforces smoothness, borrowing information from similar risk profiles. Bayesian Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs) are recovered as special cases, assuming a highly-structured prior covariance matrix. Compared to the existing literature, this paper innovates to account for the specificity of data entering insurance studies. First, proper risk exposures are included in model formulation and development. Second, parameters are estimated by minimizing deviance instead of an approximated log-likelihood. Third, categorical features that are often encountered in insurance data bases are coded with the help of an embedding method based on Burt matrices. Fourth, K-means clustering is used to reduce the dimension of the problem and create model points within large insurance portfolios. Numerical illustrations performed on publicly available insurance data sets illustrate the relevance of the GGPR approach to risk classification. Benchmarked against the classical GLM, the performances of GGPR turn out to be excellent given its reduced number of parameters. This suggests that GGPR nicely enriches the actuarial toolkit by providing preliminary predictions that can then be structured with additive scores like those entering GLMs and GAMs.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><strong><span style=\"color: #097566;\">Mots-cl\u00e9s : <\/span><\/strong>Exponential Dispersion family, Mixed models, Risk classification, Categorical embedding, Burt distance, Model points.<\/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>\n<p><b><\/b><b>Expertise: <\/b>Risk<\/p>\n<p><b>Auteurs : <\/b>Donatien Hainaut and<\/p>\n<div class=\"page\" title=\"Page 3\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p>Michel Denuit\u0084<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>\u00a0<\/p>\n<p><b>\u00c9diteur :<\/b> Detralytics<\/p>\n<p><b>Date:<\/b> April 2025<\/p>\n<p><b>Langue :<\/b> Anglais<\/p>\n<p><b>Pages:<\/b> 34<\/p>\n<p><b>R\u00e9f\u00e9rence :<\/b> Detra Note 2025-2<\/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-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=\"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-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\">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-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;\">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-4be66df e-flex e-con-boxed e-con e-parent\" data-id=\"4be66df\" 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-3e66552 elementor-widget elementor-widget-button\" data-id=\"3e66552\" 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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