{"id":4440,"date":"2019-02-12T17:08:49","date_gmt":"2019-02-12T17:08:49","guid":{"rendered":"https:\/\/detralytics.com\/?p=4440"},"modified":"2026-06-22T14:52:36","modified_gmt":"2026-06-22T14:52:36","slug":"multivariate-credibility-modelling-for-usage-based-motor-insurance-pricing-with-behavioural-data","status":"publish","type":"post","link":"https:\/\/detralytics.com\/en\/publications\/multivariate-credibility-modelling-for-usage-based-motor-insurance-pricing-with-behavioural-data\/","title":{"rendered":"Multivariate credibility modelling for usage-based motor insurance pricing with behavioural data"},"content":{"rendered":"\t\t
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Multivariate credibility modelling for usage-based motor insurance pricing with behavioural data<\/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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Pay-How-You-Drive (PHYD) or Usage-Based (UB) systems for automobile insurance provide actuaries with behavioural risk factors, such as the time of the day, average speeds and driving habits. These data are collected while the contract is in force thanks to telematic devices installed in the vehicle. They thus fall in the category of a posteriori information that becomes available after contract initiation. For this reason, they must be included in the actuarial pricing by means of credibility updating mechanisms instead of being included in the score as ordinary a priori observable features. We propose the use of multivariate mixed models to describe the joint dynamics of telematics data and claim frequencies. Future premiums, incorporating past experience can then be determined using the predictive distribution of claim characteristics given past history. This approach allows the actuary to deal with the variety of situations encountered in insurance practice, ranging from new drivers without telematics record to contracts with different seniority and drivers using their vehicle to different extent, generating varied volumes of telematics data.<\/p>

Keywords: <\/span><\/strong>Risk classification, premium calculation, driving behavior, internet of things, count data models.<\/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> Michel Denuit, Montserrat<\/p>

Guillen and Julien\u00a0Trufin<\/span><\/p>

Publication:<\/b> Annals of Actuarial Science<\/p>

Date:<\/b> February 2019<\/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\"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\"Montserrat\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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Montserrat Guillen<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Montserrat Guill\u00e9n was born in Barcelona in 1964. She received a Master of Science in Mathematics and Mathematical Statistics in 1987 and a PhD in Economics from UB in 1992. She received a MSc in Data Analysis from the University of Essex (United Kingdom). Since April, 2001 she is Chair Professor of the Department of Econometrics at the University of Barcelona. She is currently Honorary Visiting Professor in the Faculty of Actuarial Science and Insurance at City,\u00a0 University of London. She was Visiting Research faculty at the University of Texas at Austin (USA) in 1994. She was also Visiting Professor of Insurance Econometrics at the University of Paris II. She was awarded the ICREA Academia distinction in 2011 and in 2019.<\/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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We propose the use of multivariate mixed models to describe the joint dynamics of telematics data and claim frequencies.<\/p>\n","protected":false},"author":1,"featured_media":5346,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[139,133],"tags":[131],"class_list":["post-4440","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-139","category-publications","tag-detranote"],"yoast_head":"\nDetra Note : Multivariate credibility modelling<\/title>\n<meta name=\"description\" content=\"We propose the use of multivariate mixed models to describe the joint dynamics of telematics data and claim frequencies.\" \/>\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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