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Bivariate Poisson credibility model and bonus-malus scale for claim and near-claim events

Author

Listed:
  • Simon, Pierre-Alexandre

    (Université Libre de Bruxelles)

  • Trufin, Julien

    (Université Libre de Bruxelles)

  • Denuit, Michel

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

With the emergence of telematics, huge amounts of data have become available to insurers, raising the question of their integration into motor insurance pricing. Guillen (2021) and Sun (2022) introduced the notion of near-claim events, corresponding to dangerous events, which could have triggered a claim. These events typically correspond to harsh deceleration, acceleration or cornering. Based on the motor third-party liability insurance portfolio of an insurance company operating in Belgium, we highlight that deceleration events are the best candidates for characterizing near-claim events. Then, we propose to integrate these events in the pricing structure in addition to policyholder’s claim history with the help of a bivariate Poisson-LogNormal credibility model. Finally, we design an original bonus-malus scale based on both claim and near-claim events.

Suggested Citation

  • 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).
    • Handle: RePEc:aiz:louvad:2023014
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    References listed on IDEAS

    as
    1. Gao, Guangyuan & Meng, Shengwang & Wüthrich, Mario V., 2022. "What can we learn from telematics car driving data: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 185-199.
    2. Dionne, G & Vanasse, C, 1992. "Automobile Insurance Ratemaking in the Presence of Asymmetrical Information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(2), pages 149-165, April-Jun.
    3. Mercedes Ayuso & Montserrat Guillen & Jens Perch Nielsen, 2019. "Improving automobile insurance ratemaking using telematics: incorporating mileage and driver behaviour data," Transportation, Springer, vol. 46(3), pages 735-752, June.
    4. Francis Duval & Jean-Philippe Boucher & Mathieu Pigeon, 2022. "How Much Telematics Information Do Insurers Need for Claim Classification?," North American Actuarial Journal, Taylor & Francis Journals, vol. 26(4), pages 570-590, November.
    5. Michel Denuit & Yang Lu, 2021. "Wishart‐gamma random effects models with applications to nonlife insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(2), pages 443-481, June.
    6. Pinquet, Jean, 1998. "Designing Optimal Bonus-Malus Systems from Different Types of Claims," ASTIN Bulletin, Cambridge University Press, vol. 28(2), pages 205-220, November.
    7. Verschuren, Robert Matthijs, 2022. "Frequency-severity experience rating based on latent Markovian risk profiles," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 379-392.
    8. Gómez-Déniz, E., 2016. "Bivariate credibility bonus–malus premiums distinguishing between two types of claims," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 117-124.
    9. Montserrat Guillen & Jens Perch Nielsen & Ana M. Pérez-Marín & Valandis Elpidorou, 2020. "Can Automobile Insurance Telematics Predict the Risk of Near-Miss Events?," North American Actuarial Journal, Taylor & Francis Journals, vol. 24(1), pages 141-152, January.
    10. Guangyuan Gao & Shengwang Meng & Mario V. Wüthrich, 2019. "Claims frequency modeling using telematics car driving data," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(2), pages 143-162, February.
    11. Sandra Pitrebois & Michel Denuit & Jean‐François Walhin, 2006. "Multi‐Event Bonus‐Malus Scales," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(3), pages 517-528, September.
    12. Denuit, Michel & Guillen, Montserrat & Trufin, Julien, 2019. "Multivariate credibility modelling for usage-based motor insurance pricing with behavioural data," Annals of Actuarial Science, Cambridge University Press, vol. 13(2), pages 378-399, September.
    13. Park, Sojung C. & Kim, Joseph H.T. & Ahn, Jae Youn, 2018. "Does hunger for bonuses drive the dependence between claim frequency and severity?," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 32-46.
    14. Banghee So & Jean-Philippe Boucher & Emiliano A. Valdez, 2021. "Synthetic Dataset Generation of Driver Telematics," Risks, MDPI, vol. 9(4), pages 1-19, March.
    15. 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.
    16. Cheung, Eric C.K. & Ni, Weihong & Oh, Rosy & Woo, Jae-Kyung, 2021. "Bayesian credibility under a bivariate prior on the frequency and the severity of claims," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 274-295.
    17. Corradin, Alexandre & Denuit, Michel & Detyniecki, Marcin & Grari, Vincent & Sammarco, Matteo & Trufin, Julien, 2022. "Joint Modeling Of Claim Frequencies And Behavioral Signals In Motor Insurance," ASTIN Bulletin, Cambridge University Press, vol. 52(1), pages 33-54, January.
    18. Denuit, Michel & Guillen, Montserrat & Trufin, Julien, 2019. "Multivariate credibility modelling for usage-based motor insurance pricing with behavioural data," LIDAM Reprints ISBA 2019039, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Tzougas, George & Pignatelli di Cerchiara, Alice, 2021. "The multivariate mixed Negative Binomial regression model with an application to insurance a posteriori ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 602-625.
    20. Corradin, Alexandre & Denuit, Michel & Detyniecki, Marcin & Grari, Vincent & Sammarco, Matteo & Trufin, Julien, 2022. "Joint modeling of claim frequencies and behavioral signals in motor insurance," LIDAM Reprints ISBA 2022004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    21. 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.
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