{"id":4409,"date":"2020-11-21T16:41:54","date_gmt":"2020-11-21T16:41:54","guid":{"rendered":"https:\/\/detralytics.com\/?p=4409"},"modified":"2026-06-22T14:49:26","modified_gmt":"2026-06-22T14:49:26","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\/en\/publications\/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":"\t\t
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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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Abstract<\/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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Sector: <\/b>Insurance<\/b><\/p>

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

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

and Julien Trufin\u00a0<\/p>

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

Actuarial Journal<\/p>

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

Language:<\/b> English<\/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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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
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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 is a Freelance Expert at Detralytics. During her various missions, Carole has worked on various fields such as calibration of lapse rate and mortality models and a project as part of the IFRS 17 framework, aiming at identifying a Best Estimate allocation key based on some claims characteristics. Prior to joining Detralytics, Carole worked as an intern at 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 is a Scientific Advisor at Detralytics, as well as a professor in actuarial science at the Universit\u00e9 Catholique de Louvain. He has international experience as a visiting professor, and has promoted many projects in collaboration with the industry. At Detralytics, Michel coaches young talents, provides cutting-edge training, fosters innovation and oversees R&D projects.<\/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 is a Scientific Advisor at Detralytics, as well as a professor in Actuarial Science at the department of mathematics of the Universit\u00e9 Libre de Bruxelles. Julien has experience as a consultant and a strong academic background developed at prominent institutions, including Universit\u00e9 Laval (Canada), UCL, and ULB (Belgium). At Detralytics, Julien coaches young talents, provide cutting-edge training, fosters innovation and oversees R&D projects.<\/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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This article proposes an alternative to standard pricing methods based on physics-inspired neural networks (PINNs)…<\/p>\n","protected":false},"author":1,"featured_media":4656,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[138,133],"tags":[131],"class_list":["post-4409","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-138","category-publications","tag-detranote"],"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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