{"id":4409,"date":"2020-11-21T16:41:54","date_gmt":"2020-11-21T16:41:54","guid":{"rendered":"https:\/\/detralytics.com\/?p=4409"},"modified":"2026-08-21T13:31:30","modified_gmt":"2026-08-21T13:31:30","slug":"matrix-calculation-for-ultimate-and-one-year-risk-in-the-semi-markov-individual-loss-reserving-model","status":"publish","type":"post","link":"https:\/\/detralytics.com\/fr\/publication\/matrix-calculation-for-ultimate-and-one-year-risk-in-the-semi-markov-individual-loss-reserving-model\/","title":{"rendered":"Matrix calculation for ultimate and one-year risk in the semi-markov individual loss reserving model"},"content":{"rendered":"
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Matrix calculation for ultimate and one-year risk in the semi markov individual loss reserving model<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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DetraNote 2020-3<\/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
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Introduction<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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This paper proposes a multistate model with a Semi-Markov dependence structure describing the different stages in the settlement process of individual claims in general insurance. Every trajectory, from reporting to closure is combined with a modeling of individual link ratios to obtain the ultimate cost of each claim. Analytical expressions are derived for the moments of ultimate amounts whereas quantile risk measures can be obtained by simulation. In the one-year view, the proposed matrix calculations avoid the simulation-within-simulation issue and offer a tractable evaluation method. A case study illustrates the relevance of the proposed approach.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Secteur : <\/b>Assurance<\/b><\/p>

Auteurs :<\/b> Carole Bettonville,<\/p>

Louise D’Oultremont,\u00a0 Michel Denuit<\/p>

and Julien Trufin\u00a0<\/p>

\u00c9diteur :<\/b> Scandinavian<\/p>

Actuarial Journal<\/p>

Date:<\/b> November 2020<\/p>

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

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\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
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\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Carole_rond\"\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
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Carole Bettonville<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Carole est Experte Freelance chez Detralytics. Au cours de ses diff\u00e9rentes missions, elle a travaill\u00e9 sur divers sujets tels que la calibration de mod\u00e8les de taux de rachat et de mortalit\u00e9, ainsi que sur un projet dans le cadre d\u2019IFRS 17 visant \u00e0 identifier une cl\u00e9 d\u2019allocation Best Estimate bas\u00e9e sur certaines caract\u00e9ristiques de sinistres. Avant de rejoindre Detralytics, Carole a effectu\u00e9 un stage chez AXA Belgium.\u00a0<\/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

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\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Louise_rond\"\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
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Louise D'Oultremont<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Louise is People Lead and part of the Talent Consolidation Program (TCP). Prior to joining Detralytics, Louise did an internship at Axa Belgium, where she was in the risk pricing team. After a few years at Detralytics, Louise developed a solid knowledge in actuarial sciences. In particular, she worked on pricing and reserving in the fields of non-life and health 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

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\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Michel\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
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Michel Denuit<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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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&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

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\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"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
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Julien Trufin<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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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&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

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\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t<\/path><\/svg>\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\tAll 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>","protected":false},"excerpt":{"rendered":"

This article proposes an alternative to standard pricing methods based on physics-inspired neural networks (PINNs)…<\/p>","protected":false},"author":1,"featured_media":4656,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[133],"tags":[],"class_list":["post-4409","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-publication"],"yoast_head":"\nDetra Note : Matrix calculation for ultimate and one-year risk<\/title>\n<meta name=\"description\" content=\"This paper proposes a multistate model with a Semi-Markov dependence structure describing the different stages in the settlement process of individual claims in general insurance.\" \/>\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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