Bonus-Malus System Using Finite Mixture Models

  • Saeed MohammadPour Allameh Tabatabai University, Iran
  • Karzan Saeedi Allameh Tabatabai University, Iran
  • Rahim Mahmoudvand Bu-Ali Sina University, Iran
Keywords: Bonus-Malus System, Mixture model, Bayes theorem

Abstract

There is a vast literature on Bonus-Malus System (BMS), in which a policyholders responsible for positive claims will be penalised by a malus and the policyholders who had no claim will be rewarded by a bonus. In this paper, we present an optimal BMS using finite mixture models.  We conduct a numerical study to compare the new model with the current BMS that use finite mixture models.

References

Denuit, M. and Ph. Lambert (2001). Smoothed NPML estimation of the risk distribution underlying Bonus-Malus systems. Proceedings of the Casualty Actuarial Society, 88, 142–174.

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, 1–22.

Gomez-Deniz, E., Vaquez-Polo, F.J., Perez-Sanchez, J.M. (2004). A note on mixture prior distributions with applications in actuarial statistic. Estudios de Economia Aplicada, 22 (2), 1–15.

Tzougas, G., Vrontos, S., and Frangos, N. (2014). Optimal Bonus-Malus Systems using Finite Mixture Models. ASTIN Bulletin, 44, 417–444.

Peter Macdonald and with contributions from Juan Du (2012). mixdist: Finite Mixture Distribution Models. R package version 0.5-4. http://CRAN.R-project.org/package=mixdist

Mahmoudvand, R., and Hassani, H. (2009). Generalized bonus-malus systems with a frequency and a severity component on an individual basis in automobile insurance. ASTIN Bulletin, 39(01), 307-315.

Mahmoudvand, R., Tan, C. & Abbasi, N. (2017). Adjusting the Premium Relativities in a Bonus-Malus System: An Integrated Approach Using the First Claim Time and the Number of Claims. Asia-Pacific Journal of Risk and Insurance, Forthcoming, doi:10.1515/apjri-2016-0038

Weinberg, G.V., Finch, D. (2012). Analysis of a Pareto Mixture Distribution for Maritime Surveillance Radar. Journal of Electrical and Computer Engineering, http://dx.doi.org/10.1155/2012/382979.

Published
2017-08-29
How to Cite
MohammadPour, S., Saeedi, K., & Mahmoudvand, R. (2017). Bonus-Malus System Using Finite Mixture Models. Statistics, Optimization & Information Computing, 5(3), 179-187. https://doi.org/10.19139/soic.v5i3.264
Section
Research Articles