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Using the Poisson Inverse Gaussian in Bonus-Malus Systems

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  • Tremblay, Luc

Abstract

In this paper, we will cover the bonus-malus system in automobile insurance. Bonus-malus systems are based on the distribution of the number of car accidents. Therefore, the modelling and fitting of that distribution are considered. Fitting of data is done using the Poisson inverse Gaussian distribution, which shows a good fit. Building the bonus system is done by minimizing the insurer's risk, according to Lemaire's (1985) bonus system.

Suggested Citation

  • Tremblay, Luc, 1992. "Using the Poisson Inverse Gaussian in Bonus-Malus Systems," ASTIN Bulletin, Cambridge University Press, vol. 22(1), pages 97-106, May.
    • Handle: RePEc:cup:astinb:v:22:y:1992:i:01:p:97-106_00
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    Cited by:

    1. Azaare Jacob & Zhao Wu, 2020. "An Alternative Pricing System through Bayesian Estimates and Method of Moments in a Bonus-Malus Framework for the Ghanaian Auto Insurance Market," JRFM, MDPI, vol. 13(7), pages 1-15, July.
    2. Farouk Mselmi, 2022. "Generalized linear model for subordinated Lévy processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 772-801, June.
    3. Tan, Chong It & Li, Jackie & Li, Johnny Siu-Hang & Balasooriya, Uditha, 2015. "Optimal relativities and transition rules of a bonus–malus system," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 255-263.
    4. Yang Lu, 2018. "Dynamic Frailty Count Process in Insurance: A Unified Framework for Estimation, Pricing, and Forecasting," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(4), pages 1083-1102, December.
    5. Zhu, Rong & Joe, Harry, 2009. "Modelling heavy-tailed count data using a generalised Poisson-inverse Gaussian family," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1695-1703, August.
    6. Emilio Gomez-deniz & Francisco Vazquez-polo, 2005. "Modelling uncertainty in insurance Bonus-Malus premium principles by using a Bayesian robustness approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 771-784.
    7. A.Hernández-Bastida & J. M. Pérez–Sánchez & E. Gómez-Deniz, 2007. "Bayesian Analysis Of The Compound Collective Model: The Net Premium Principle With Exponential Poisson And Gamma–Gamma Distributions," FEG Working Paper Series 07/03, Faculty of Economics and Business (University of Granada).
    8. Emilio Gomez-Deniz & Enrique Calderin-Ojeda, 2010. "A study of Bayesian local robustness with applications in actuarial statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1537-1546.
    9. 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.
    10. 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.
    11. Serpil Bülbül & Kemal Baykal, 2016. "Optimal Bonus-Malus System Design in Motor Third-Party Liability Insurance in Turkey: Negative Binomial Model," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 8(8), pages 205-205, August.

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