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Bonus‐Malus Scales in Segmented Tariffs With Stochastic Migration Between Segments

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  • Natacha Brouhns
  • Montserrat Guillén
  • Michel Denuit
  • Jean Pinquet

Abstract

This article proposes a computer‐intensive methodology to build bonus‐malus scales in automobile insurance. The claim frequency model is taken from Pinquet, Guillén, and Bolancé (2001). It accounts for overdispersion, heteroskedasticity, and dependence among repeated observations. Explanatory variables are taken into account in the determination of the relativities, yielding an integrated automobile ratemaking scheme. In that respect, it complements the study of Taylor (1997).

Suggested Citation

  • Natacha Brouhns & Montserrat Guillén & Michel Denuit & Jean Pinquet, 2003. "Bonus‐Malus Scales in Segmented Tariffs With Stochastic Migration Between Segments," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 577-599, December.
    • Handle: RePEc:bla:jrinsu:v:70:y:2003:i:4:p:577-599
    DOI: 10.1046/j.0022-4367.2003.00066.x
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    1. Dionne, Georges & Vanasse, Charles, 1989. "A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 199-212, November.
    2. 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.
    3. Sundt, Bjorn, 1988. "Credibility estimators with geometric weights," Insurance: Mathematics and Economics, Elsevier, vol. 7(2), pages 113-122, April.
    4. Renshaw, Arthur E., 1994. "Modelling the Claims Process in the Presence of Covariates," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 265-285, November.
    5. Pinquet, Jean & Guillén, Montserrat & Bolancé, Catalina, 2001. "Allowance for the Age of Claims in Bonus-Malus Systems," ASTIN Bulletin, Cambridge University Press, vol. 31(2), pages 337-348, November.
    6. 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.
    7. de Lourdes Centeno, Maria & Manuel Andrade e Silva, Joao, 2001. "Bonus systems in an open portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 341-350, June.
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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. Oh, Rosy & Lee, Kyung Suk & Park, Sojung C. & Ahn, Jae Youn, 2020. "Double-counting problem of the bonus–malus system," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 141-155.
    3. Tzougas, George & Yik, Woo Hee & Mustaqeem, Muhammad Waqar, 2019. "Insurance ratemaking using the Exponential-Lognormal regression model," LSE Research Online Documents on Economics 101729, London School of Economics and Political Science, LSE Library.
    4. Florian Schreiber, 2017. "Identification of customer groups in the German term life market: a benefit segmentation," Annals of Operations Research, Springer, vol. 254(1), pages 365-399, July.
    5. Tsyganov, Aleksander & Baskakov, Valery & Yazykov, Andrey & Sheparnev, Nikolay & Yanenko, Evgeny & Grysenkova, Yulia, 2019. "The impact of the bonus-malus system on the insurance ratemaking in the system of compulsory insurance of the responsibility of transport owners in Russia," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 56, pages 123-141.
    6. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2014. "Optimal Bonus-Malus Systems using finite mixture models," LSE Research Online Documents on Economics 70919, London School of Economics and Political Science, LSE Library.
    7. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2018. "Bonus-Malus systems with two component mixture models arising from different parametric families," LSE Research Online Documents on Economics 84301, London School of Economics and Political Science, LSE Library.
    8. Pinquet, Jean, 2020. "Positivity properties of the ARFIMA(0,d,0) specifications and credibility analysis of frequency risks," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 159-165.
    9. Tzougas, George, 2020. "EM estimation for the Poisson-Inverse Gamma regression model with varying dispersion: an application to insurance ratemaking," LSE Research Online Documents on Economics 106539, London School of Economics and Political Science, LSE Library.
    10. Bolancé, Catalina & Guillén, Montserrat & Pinquet, Jean, 2008. "On the link between credibility and frequency premium," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 209-213, October.
    11. 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.
    12. George Tzougas, 2020. "EM Estimation for the Poisson-Inverse Gamma Regression Model with Varying Dispersion: An Application to Insurance Ratemaking," Risks, MDPI, vol. 8(3), pages 1-23, September.
    13. Bermúdez, Lluís & Karlis, Dimitris, 2012. "A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3988-3999.
    14. 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.
    15. Zhao, Xiaobing & Zhou, Xian, 2012. "Copula models for insurance claim numbers with excess zeros and time-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 191-199.
    16. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    17. 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.
    18. Tzougas, George & Karlis, Dimitris & Frangos, Nicholas, 2017. "Confidence intervals of the premiums of optimal Bonus Malus Systems," LSE Research Online Documents on Economics 70926, London School of Economics and Political Science, LSE Library.
    19. Lluís Bermúdez & Dimitris Karlis & Isabel Morillo, 2020. "Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models," Risks, MDPI, vol. 8(1), pages 1-13, January.
    20. Bermúdez i Morata, Lluís, 2009. "A priori ratemaking using bivariate Poisson regression models," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 135-141, February.
    21. Youn Ahn, Jae & Jeong, Himchan & Lu, Yang, 2021. "On the ordering of credibility factors," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 626-638.
    22. Tan, Chong It, 2016. "Varying transition rules in bonus–malus systems: From rules specification to determination of optimal relativities," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 134-140.
    23. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.

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