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Exposure as Duration and Distance in Telematics Motor Insurance Using Generalized Additive Models

Author

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  • Jean-Philippe Boucher

    (Département de Mathématiques, Université du Québec à Montréal (UQAM); Montréal, QC H3C 3P8, Canada)

  • Steven Côté

    (Département de Mathématiques, Université du Québec à Montréal (UQAM); Montréal, QC H3C 3P8, Canada)

  • Montserrat Guillen

    (Department of Econometrics, Riskcenter-IREA, Universitat de Barcelona, 08007 Barcelona, Spain)

Abstract

In Pay-As-You-Drive (PAYD) automobile insurance, the premium is fixed based on the distance traveled, while in usage-based insurance (UBI) the driving patterns of the policyholder are also considered. In those schemes, drivers who drive more pay a higher premium compared to those with the same characteristics who drive only occasionally, because the former are more exposed to the risk of accident. In this paper, we analyze the simultaneous effect of the distance traveled and exposure time on the risk of accident by using Generalized Additive Models (GAM). We carry out an empirical application and show that the expected number of claims (1) stabilizes once a certain number of accumulated distance-driven is reached and (2) it is not proportional to the duration of the contract, which is in contradiction to insurance practice. Finally, we propose to use a rating system that takes into account simultaneously exposure time and distance traveled in the premium calculation. We think that this is the trend the automobile insurance market is going to follow with the eruption of telematics data.

Suggested Citation

  • Jean-Philippe Boucher & Steven Côté & Montserrat Guillen, 2017. "Exposure as Duration and Distance in Telematics Motor Insurance Using Generalized Additive Models," Risks, MDPI, vol. 5(4), pages 1-23, September.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:4:p:54-:d:113169
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    References listed on IDEAS

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    1. Jean‐Philippe Boucher & Michel Denuit & Montserrat Guillen, 2009. "Number of Accidents or Number of Claims? An Approach with Zero‐Inflated Poisson Models for Panel Data," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(4), pages 821-846, December.
    2. Paefgen, Johannes & Staake, Thorsten & Fleisch, Elgar, 2014. "Multivariate exposure modeling of accident risk: Insights from Pay-as-you-drive insurance data," Transportation Research Part A: Policy and Practice, Elsevier, vol. 61(C), pages 27-40.
    3. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
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    Citations

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    Cited by:

    1. Guillen, Montserrat & Bermúdez, Lluís & Pitarque, Albert, 2021. "Joint generalized quantile and conditional tail expectation regression for insurance risk analysis," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 1-8.
    2. Montserrat Guillen & Jens Perch Nielsen & Ana M. Pérez‐Marín, 2021. "Near‐miss telematics in motor insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(3), pages 569-589, September.
    3. Meng, Shengwang & Gao, Yaqian & Huang, Yifan, 2022. "Actuarial intelligence in auto insurance: Claim frequency modeling with driving behavior features and improved boosted trees," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 115-127.
    4. Zhiyu Quan & Changyue Hu & Panyi Dong & Emiliano A. Valdez, 2024. "Improving Business Insurance Loss Models by Leveraging InsurTech Innovation," Papers 2401.16723, arXiv.org.
    5. Francis Duval & Jean‐Philippe Boucher & Mathieu Pigeon, 2023. "Enhancing claim classification with feature extraction from anomaly‐detection‐derived routine and peculiarity profiles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(2), pages 421-458, June.
    6. Ma, Yu-Luen & Zhu, Xiaoyu & Hu, Xianbiao & Chiu, Yi-Chang, 2018. "The use of context-sensitive insurance telematics data in auto insurance rate making," Transportation Research Part A: Policy and Practice, Elsevier, vol. 113(C), pages 243-258.
    7. Tingting Chen & Anthony Francis Desmond & Peter Adamic, 2023. "Generalized Additive Modelling of Dependent Frequency and Severity Distributions for Aggregate Claims," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 12(4), pages 1-1.
    8. Simon, Pierre-Alexandre & Trufin, Julien & Denuit, Michel, 2023. "Bivariate Poisson credibility model and bonus-malus scale for claim and near-claim events," LIDAM Discussion Papers ISBA 2023014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Omid Ghaffarpasand & Mark Burke & Louisa K. Osei & Helen Ursell & Sam Chapman & Francis D. Pope, 2022. "Vehicle Telematics for Safer, Cleaner and More Sustainable Urban Transport: A Review," Sustainability, MDPI, vol. 14(24), pages 1-20, December.
    10. Gao, Guangyuan & Wüthrich, Mario V. & Yang, Hanfang, 2019. "Evaluation of driving risk at different speeds," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 108-119.

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