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Optimal Bonus-Malus Systems Using Finite Mixture Models

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  • Tzougas, George
  • Vrontos, Spyridon
  • Frangos, Nicholas

Abstract

This paper presents the design of optimal Bonus-Malus Systems using finite mixture models, extending the work of Lemaire (1995; Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance. Norwell, MA: Kluwer) and Frangos and Vrontos (2001; Frangos, N. and Vrontos, S. (2001) Design of optimal bonus-malus systems with a frequency and a severity component on an individual basis in automobile insurance. ASTIN Bulletin, 31(1), 1–22). Specifically, for the frequency component we employ finite Poisson, Delaporte and Negative Binomial mixtures, while for the severity component we employ finite Exponential, Gamma, Weibull and Generalized Beta Type II mixtures, updating the posterior probability. We also consider the case of a finite Negative Binomial mixture and a finite Pareto mixture updating the posterior mean. The generalized Bonus-Malus Systems we propose, integrate risk classification and experience rating by taking into account both the a priori and a posteriori characteristics of each policyholder.

Suggested Citation

  • Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2014. "Optimal Bonus-Malus Systems Using Finite Mixture Models," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 417-444, May.
    • Handle: RePEc:cup:astinb:v:44:y:2014:i:02:p:417-444_00
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    Citations

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    Cited by:

    1. Yang Lu, 2019. "Flexible (panel) regression models for bivariate count–continuous data with an insurance application," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1503-1521, October.
    2. 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.
    3. Tzougas, George & Karlis, Dimitris, 2020. "An EM algorithm for fitting a new class of mixed exponential regression models with varying dispersion," LSE Research Online Documents on Economics 104027, London School of Economics and Political Science, LSE Library.
    4. Despoina Makariou & Pauline Barrieu & George Tzougas, 2021. "A Finite Mixture Modelling Perspective for Combining Experts’ Opinions with an Application to Quantile-Based Risk Measures," Risks, MDPI, vol. 9(6), pages 1-25, June.
    5. Makariou, Despoina & Barrieu, Pauline & Tzougas, George, 2021. "A finite mixture modelling perspective for combining experts’ opinions with an application to quantile-based risk measures," LSE Research Online Documents on Economics 110763, London School of Economics and Political Science, LSE Library.
    6. 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.
    7. 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.
    8. Martinek, László & Arató, N. Miklós, 2019. "An approach to merit rating by means of autoregressive sequences," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 205-217.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Olena Ragulina, 2017. "Bonus--malus systems with different claim types and varying deductibles," Papers 1707.00917, arXiv.org.
    14. Verschuren, Robert Matthijs, 2022. "Frequency-severity experience rating based on latent Markovian risk profiles," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 379-392.
    15. Hansjörg Albrecher & Martin Bladt & Eleni Vatamidou, 2021. "Efficient Simulation of Ruin Probabilities When Claims are Mixtures of Heavy and Light Tails," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1237-1255, December.
    16. 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.

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