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    "slug": "in-processing-of-actuarial-and-equity-fairness-constraints-for-neural-networks",
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    "title": {
        "rendered": "In-processing of actuarial and equity fairness constraints for Neural networks"
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        "rendered": "<div data-elementor-type=\"wp-post\" data-elementor-id=\"5774\" class=\"elementor elementor-5774\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b65d126 e-flex e-con-boxed e-con e-parent\" data-id=\"b65d126\" 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-cc676cc elementor-widget elementor-widget-heading\" data-id=\"cc676cc\" 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\">In-processing of actuarial and equity fairness constraints for neural networks<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d54ca97 elementor-widget elementor-widget-heading\" data-id=\"d54ca97\" 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\">Detra Note 2025-4<\/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\/2025\/08\/Detralytics_DetraNote-2025-4_Neural-Networks.pdf\" target=\"_blank\">\n\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"764\" height=\"1080\" src=\"https:\/\/detralytics.com\/wp-content\/uploads\/2025\/08\/DETRAnote_EN-2025-4-764x1080.jpg\" class=\"elementor-animation-grow attachment-large size-large wp-image-5775\" alt=\"DetraNote 2025-4\" srcset=\"https:\/\/detralytics.com\/wp-content\/uploads\/2025\/08\/DETRAnote_EN-2025-4-764x1080.jpg 764w, https:\/\/detralytics.com\/wp-content\/uploads\/2025\/08\/DETRAnote_EN-2025-4-768x1086.jpg 768w, https:\/\/detralytics.com\/wp-content\/uploads\/2025\/08\/DETRAnote_EN-2025-4-1086x1536.jpg 1086w, https:\/\/detralytics.com\/wp-content\/uploads\/2025\/08\/DETRAnote_EN-2025-4.jpg 1240w\" sizes=\"(max-width: 764px) 100vw, 764px\" \/>\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\/08\/Detralytics_DetraNote-2025-4_Neural-Networks.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\">Download<\/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\">Abstract<\/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\"><div class=\"layoutArea\"><div class=\"column\"><p class=\"p1\">This article introduces a novel in-processing method for integrating actuarial and equity fairness into neural networks used for actuarial valuation. We consider one primary network penalized during training to ensure balanced predictions (actuarial fairness) and independence from sensitive features (equity fairness). Global and local actuarial equilibrium is obtained by aligning the inter-quantile averages of predicted and observed responses. Meanwhile, a second auxiliary network penalizes the primary network for discriminatory predictions. The combined training algorithm effectively preserves predictive accuracy while mitigating discrimination. Numerical illustrations on real-world datasets demonstrate the method\u2019s efficacy in achieving fair and reliable insurance pricing models.<\/p><\/div><\/div><\/div><p><strong><span style=\"color: #097566;\">Keywords: <\/span><\/strong>neural network, equity fairness, actuarial fairness, non-life pricing.<\/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>Sector: <\/b>Insurance<\/p><p><b><\/b><b>Expertise: <\/b>Non-life pricing<\/p><p><b>Authors: <\/b>Donatien Hainaut<\/p><p><b>Publisher:<\/b> Detralytics<\/p><p><b>Date:<\/b> April 2025<\/p><p><b>Language:<\/b> English<\/p><p><b>Pages:<\/b> 27<\/p><p><b>Reference :<\/b> Detra Note 2025-4<\/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\">About the authors<\/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 is a Scientific Advisor at Detralytics and a professor at UCLouvain (Belgium), where he serves as the Director of the Master\u2019s program in Data Science with a statistical orientation. Prior to this, he held several academic positions, including Associate Professor at Rennes School of Business and ENSAE in Paris. He also has extensive industry experience, having worked as a Risk Officer, Quantitative Analyst, and ALM Officer.<\/p><p class=\"has-text-color has-link-color wp-elements-319687f5e483df5041193c0b748e25dd\">Donatien is a Qualified Actuary and holds a PhD in the field of Asset and Liability Management. His current research focuses on contagion mechanisms in stochastic processes and the applications of neural networks in insurance.<\/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-2d217fc e-flex e-con-boxed e-con e-parent\" data-id=\"2d217fc\" 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-aaa2031 elementor-widget elementor-widget-button\" data-id=\"aaa2031\" 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\/en\/publications\/\">\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-fas-arrow-left\" viewbox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M257.5 445.1l-22.2 22.2c-9.4 9.4-24.6 9.4-33.9 0L7 273c-9.4-9.4-9.4-24.6 0-33.9L201.4 44.7c9.4-9.4 24.6-9.4 33.9 0l22.2 22.2c9.5 9.5 9.3 25-.4 34.3L136.6 216H424c13.3 0 24 10.7 24 24v32c0 13.3-10.7 24-24 24H136.6l120.5 114.8c9.8 9.3 10 24.8.4 34.3z\"><\/path><\/svg>\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">All Publications<\/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\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>",
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        "rendered": "<p>This paper proposes a new approach to risk classification based on Generalized Gaussian Pro-cess Regression (GGPR).<\/p>",
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