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Accounting for Individual Over-Dispersion in a Bonus-Malus Automobile Insurance System

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  • Shengwang, Meng
  • Wei, Yuan
  • Whitmore, G.A.

Abstract

Individual automobile insurance claims are characterized by over-dispersion relative to the Poisson model. In addition, claim propensities vary among individuals in any insurance portfolio. This paper presents a model which takes account of both characteristics. The model employs the negative-binomial distribution as the distribution for individual-level claims and a Pareto distribution as the distribution for claim propensities within the portfolio. The paper shows that the resulting model is tractable and has a number of attractive properties which make it suitable for this application. The fit of the model to actual claim numbers for automobile third party liability insurance is examined and found acceptable. Bayes theorem is then applied to this model to calculate illustrative optimal premiums under the Bonus-Malus System (BMS).

Suggested Citation

  • Shengwang, Meng & Wei, Yuan & Whitmore, G.A., 1999. "Accounting for Individual Over-Dispersion in a Bonus-Malus Automobile Insurance System," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 327-337, November.
    • Handle: RePEc:cup:astinb:v:29:y:1999:i:02:p:327-337_01
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    Cited by:

    1. Tzougas, George & Hoon, W. L. & Lim, J. M., 2019. "The negative binomial-inverse Gaussian regression model with an application to insurance ratemaking," LSE Research Online Documents on Economics 101728, London School of Economics and Political Science, LSE Library.
    2. Sarabia, José María & Gómez-Déniz, Emilio & Prieto, Faustino & Jordá, Vanesa, 2016. "Risk aggregation in multivariate dependent Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 154-163.
    3. 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.
    4. Villar Frexedas, Oscar & Vayá, Esther, 2005. "Financial Contagion between Economies: an Exploratory Spatial Analysis/Contagio financiero entre economías: Un análisis exploratorio espacial," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 23, pages 151-165, Abril.

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