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A Priori Ratemaking Selection Using Multivariate Regression Models Allowing Different Coverages in Auto Insurance

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  • Emilio Gómez-Déniz

    (Department of Quantitative Methods, Faculty of Economics, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain)

  • Enrique Calderín-Ojeda

    (Department of Economics, University of Melbourne, Melbourne 3031, Australia)

Abstract

A comprehensive auto insurance policy usually provides the broadest protection for the most common events for which the policyholder would file a claim. On the other hand, some insurers offer extended third-party car insurance to adapt to the personal needs of every policyholder. The extra coverage includes cover against fire, natural hazards, theft, windscreen repair, and legal expenses, among some other coverages that apply to specific events that may cause damage to the insured’s vehicle. In this paper, a multivariate distribution, based on a conditional specification, is proposed to account for different numbers of claims for different coverages. Then, the premium is computed for each type of coverage separately rather than for the total claims number. Closed-form expressions are given for moments and cross-moments, parameter estimates, and for a priori premiums when different premiums principles are considered. In addition, the severity of claims can be incorporated into this multivariate model to derive multivariate claims’ severity distributions. The model is extended by developing a zero-inflated version. Regression models for both multivariate families are derived. These models are used to fit a real auto insurance portfolio that includes five types of coverage. Our findings show that some specific covariates are statistically significant in some coverages, yet they are not so for others.

Suggested Citation

  • Emilio Gómez-Déniz & Enrique Calderín-Ojeda, 2021. "A Priori Ratemaking Selection Using Multivariate Regression Models Allowing Different Coverages in Auto Insurance," Risks, MDPI, vol. 9(7), pages 1-18, July.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:7:p:137-:d:597628
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    References listed on IDEAS

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    1. Cummins, J. David & Wiltbank, Laurel J., 1984. "A Multivariate Model of the Total Claims Process," ASTIN Bulletin, Cambridge University Press, vol. 14(1), pages 45-52, April.
    2. Liu, Yin & Tian, Guo-Liang, 2015. "Type I multivariate zero-inflated Poisson distribution with applications," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 200-222.
    3. Zhang, Pengcheng & Calderin, Enrique & Li, Shuanming & Wu, Xueyuan, 2020. "On the Type I multivariate zero-truncated hurdle model with applications in health insurance," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 35-45.
    4. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, vol. 4(1), pages 1-36, February.
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