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Multivariate credibility modelling for usage-based motor insurance pricing with behavioural data

Published online by Cambridge University Press:  12 February 2019

Michel Denuit ,
Montserrat Guillen  and
Julien Trufin
Michel Denuit
Affiliation:
Institute of Statistics, Biostatistics and Actuarial Science, Louvain Institute of Data Analysis and Modeling, UC Louvain, 1348 Louvain-la-Neuve, Belgium
Montserrat Guillen
Affiliation:
Riskcenter, Department of Econometrics, Universitat de Barcelona, 08034 Barcelona, Spain
Julien Trufin*
Affiliation:
Department of Mathematics, Université Libre de Bruxelles (ULB), 1050 Bruxelles, Belgium
*
*Correspondence to: Julien Trufin. E-mail: [email protected]
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Abstract

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 other driving habits. These data are collected while the contract is in force with the help of 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 incorporated in the score as ordinary a priori observable features. This paper proposes 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.

Keywords

Risk classificationPremium calculationDriving behaviourInternet of thingsCount data models
Type
Paper
Information
Annals of Actuarial Science , Volume 13 , Issue 2 , September 2019 , pp. 378 - 399
Copyright
© Institute and Faculty of Actuaries 2019 

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References

Ayuso, M., Guillen, M. & Pérez-Marín, A.M. (2016). Telematics and gender discrimination: Some usage-based evidence on whether men’s risk of accidents differs from women’s. Risks, 4, 10.Google Scholar
Ayuso, M., Guillen, M. & Nielsen, J.P. (2018). Improving automobile insurance ratemaking using telematics: incorporating mileage and driver behaviour data. Transportation, in press.Google Scholar
Baecke, P. & Bocca, L. (2017). The value of vehicle telematics data in insurance risk selection processes. Decision Support Systems, 98, 69–79.Google Scholar
Bolderdijk, J.W., Knockaert, J., Steg, E.M. & Verhoef, E.T. (2011). Effects of Pay-As-You-Drive vehicle insurance on young drivers’ speed choice: Results of a Dutch field experiment. Accident Analysis and Prevention, 43, 1181–1186.Google Scholar
Boucher, J.P., Pérez-Marín, A.M. & Santolino, M. (2013). Pay-as-you-drive insurance: The effect of the kilometers on the risk of accident. Anales del Instituto de Actuarios Españoles, 19, 135–154.Google Scholar
Denuit, M., Marechal, X., Pitrebois, S. & Walhin, J.-F. (2007). Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems. Wiley, New York.Google Scholar
Faraway, J.J. (2016). Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, 2nd edition. CRC, Boca Raton, FL.Google Scholar
Gao, G., Meng, S. & Wuthrich, M.V. (2018). Claims frequency modeling using telematics car driving data. Available at SSRN https://ssrn.com/abstract=3102371.Google Scholar
Guillen, M., Nielsen, J.P., Ayuso, M. & Pérez-Marín, A.M. (2018). The use of telematics devices to improve automobile insurance rates. Risk Analysis, accepted (in press).Google Scholar
Guillen, M. & Pérez-Marín, A.M. (2018). The contribution of Usage-Based data analytics to benchmark semi-autonomous vehicle insurance. In Mathematical and Statistical Methods for Actuarial Sciences and Finance (pp. 419–423). Springer.Google Scholar
Jin, W., Deng, Y., Jiang, H., Xie, Q., Shen, W. & Han, W. (2018). Latent class analysis of accident risks in usage-based insurance: evidence from Beijing. Accident Analysis and Prevention, 115, 79–88.Google Scholar
Lemaire, J. (1995). Bonus-Malus Systems in Automobile Insurance. Kluwer Academic Publisher, Boston.Google Scholar
Tselentis, D.I., Yannis, G. & Vlahogianni, E.I. (2017). Innovative motor insurance schemes: a review of current practices and emerging challenges. Accident Analysis and Prevention, 98, 139–148.Google Scholar
Verbelen, R., Antonio, K. & Claeskens, G. (2018). Unravelling the predictive power of telematics data in car insurance pricing. Journal of the Royal Statistical Society: Series C (Applied Statistics), 67, 1275–1304.Google Scholar
Weidner, W., Transchel, F.W.G. & Weidner, R. (2016). Classification of scale-sensitive telematic observables for risk individual pricing. European Actuarial Journal, 6, 3–24.Google Scholar
Weidner, W., Transchel, F.W. & Weidner, R. (2017). Telematic driving profile classification in car insurance pricing. Annals of Actuarial Science, 11, 213–236.Google Scholar
Williams, A.F. (1985). Nighttime driving and fatal crash involvement of teenagers. Accident Analysis and Prevention, 17, 1–5.Google Scholar
Wüthrich, M.V. (2017). Covariate selection from telematics car driving data. European Actuarial Journal, 7, 89–108.Google Scholar
Wood, S.N. (2017). Generalized Additive Models: An Introduction with R, 2nd edition. Chapman and Hall/CRC, Boca Raton, FL.Google Scholar