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Home and Motor insurance joined at a household level using multivariate credibility

Author

Listed:
  • Pechon, Florian
  • Denuit, Michel

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

  • Trufin, Julien

    (ULB)

Abstract

Actuarial ratemaking is usually performed at product and guarantee level, meaning that each product and guarantee is considered in isolation. Moreover, independence between policyholders is generally assumed. In this paper, we propose a multivariate Poisson mixture, with random effects correlated using a hierarchical structure, to accommodate for the dependence that may exist between unobserved risk factors across Home and Motor insurance and between policyholders from the same household. The hierarchical structure accounts for the fact that Home insurance covers the whole household, whereas Motor insurance policies are subscribed by specific policyholders within the household. The model allows to periodically correct the a priori expected claim frequencies using the reported number of claims in any of the considered products. Applications show that the impact of the number of claims reported in Motor insurance on the number of claims expected in Home insurance is larger than the other way around. Moreover, an out-of-sample analysis validates an improved predictive power. Also, the model allows to identify more rapidly the riskiest households.

Suggested Citation

  • Pechon, Florian & Denuit, Michel & Trufin, Julien, 2021. "Home and Motor insurance joined at a household level using multivariate credibility," LIDAM Reprints ISBA 2021007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2021007
    DOI: https://doi.org/10.1017/s1748499520000160
    Note: In: Annals of Actuarial Science, Vol. 15, no.1, p. 82-114 (2021)
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    Cited by:

    1. Tzougas, George & Makariou, Despoina, 2022. "The multivariate Poisson-Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," LSE Research Online Documents on Economics 117197, London School of Economics and Political Science, LSE Library.
    2. Chen, Zezhun Chen & Dassios, Angelos & Tzougas, George, 2024. "EM estimation for bivariate mixed poisson INAR(1) claim count regression models with correlated random effects," LSE Research Online Documents on Economics 118826, London School of Economics and Political Science, LSE Library.
    3. Zezhun Chen & Angelos Dassios & George Tzougas, 2023. "Multivariate mixed Poisson Generalized Inverse Gaussian INAR(1) regression," Computational Statistics, Springer, vol. 38(2), pages 955-977, June.
    4. George Tzougas & Despoina Makariou, 2022. "The multivariate Poisson‐Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 25(4), pages 401-417, December.
    5. Raphael Iten & Joël Wagner & Angela Zeier Röschmann, 2021. "On the Identification, Evaluation and Treatment of Risks in Smart Homes: A Systematic Literature Review," Risks, MDPI, vol. 9(6), pages 1-30, June.

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