Claim Modeling and Insurance Premium Pricing Under A Bonus–Malus System in Motor Insurance
References
- Akaike, H. (1974). A new look at the statistical model identification, IEEE Transactions on Automatic Control 19(6): 716–723.
- Bulbul, S. and Baykal, K. (2016). Optimal bonus malus system design in motor third party liability insurance in Turkey: Negative binomial model, International Journal of Economics and Finance 8(8): 205–211.
- Bühlmann, H. (1970). Mathematical Methods in Risk Theory, Springer, New York.
- Cojocaru, I. (2017). Ruin probabilities in multivariate risk models with periodic common shock, Scandinavian Actuarial Journal 2017(2): 159–174.
- De Jong, P. and Heller, G. (2008). Generalized Linear Models for Insurance Data, Cambridge University Press, New York.
- Emad, A. and Ali, I. (2016). Bayesian approach for bonus-malus systems with Gamma distributed claim severities in vehicles insurance, British Journal of Economics, Management, and Trade 14(1): 1–9.
- 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.
- Grzegorzewski, P., Hryniewicz, O. and Romaniuk, M. (2020). Flexible resampling for fuzzy data, International Journal of Applied Mathematics and Computer Science 30(2): 281–297, DOI: 10.34768/amcs-2020-0022.
- Grzegorzewski, P. and Romaniuk, M. (2022). Bootstrap methods for epistemic fuzzy data, International Journal of Applied Mathematics and Computer Science 32(2): 285–297, DOI: 10.34768/amcs-2022-0021.
- Karlis, D. and Xekalaki, E. (2005). Mixed Poisson distributions, International Statistical Review 73(1): 35–58.
- Lemaire, J. (1995). Bonus-malus systems in automobile insurance, Insurance: Mathematics and Economics 3(16): 227.
- Lindley, D. (1958). Fiducial distributions and Bayes’ theorem, Journal of the Royal Statistical Society B 20(1): 102–107.
- Matsui, M. and Rolski, T. (2016). Prediction in a mixed Poisson cluster model, Stochastic Models 32(3): 460–480.
- Mert, M. and Saykan, Y. (2005). On a bonus-malus system where the claim frequency distribution is geometric and the claim severity distribution is Pareto, Hacettepe Journal of Mathematics and Statistics 34(1): 75–81.
- Moumeesri, A., Klongdee, W. and Pongsart, T. (2020). Bayesian bonus-malus premium with Poisson–Lindley distributed claim frequency and lognormal-Gamma distributed claim severity in automobile insurance, WSEAS Transactions on Mathematics 19(46): 443–451.
- Moumeesri, A. and Pongsart, T. (2022). Bonus-malus premiums based on claim frequency and the size of claims, Risks 10(9): 181.
- Nedjar, S. and Zeghdoudi, H. (2016). On Gamma Lindley distribution: Properties and simulations, Journal of Computational and Applied Mathematics 298: 167–174.
- Ni, W., Constantinescu, C. and Pantelous, A. (2014). Bonus-malus systems with Weibull distributed claim severities, Annals of Actuarial Science 8(2): 217–233.
- Nowak, P. and Romaniuk, M. (2013). A fuzzy approach to option pricing in a Levy process setting, International Journal of Applied Mathematics and Computer Science 23(3): 613–622, DOI: 10.2478/amcs-2013-0046.
- Pongsart, T., Moumeesri, A., Mayureesawan, T. and Phaphan, W. (2021). Computing Bayesian bonus-malus premium distinguishing among different multiple types of claims, Lobachevskii Journal of Mathematics 42(13): 3208–3217.
- Romaniuk, M. (2017). Analysis of the insurance portfolio with an embedded catastrophe bond in a case of uncertain parameter of the insurer’s share, in A. Grzech et al. (Eds), Information Systems Architecture and Technology: Proceedings of 37th International Conference on Information Systems Architecture and Technology, ISAT 2016. Part IV: Advances in Intelligent Systems and Computing, Springer, Berlin/Heidelberg, pp. 33–43.
- Sankaran, M. (1970). The discrete Poisson–Lindley distribution, Biometrics 26(1): 145–149.
- Shanker, R. and Mishra, A. (2013). A two-parameter Lindley distribution, Statistics in Transition—New Series 14(1): 45–56.
- Shanker, R. and Mishra, A. (2014). A two-parameter Poisson–Lindley distribution, International Journal of Statistics and Systems 9(1): 79–85.
- Stone, M. (1979). Comments on model selection criteria of Akaike and Schwartz, Journal of the Royal Statistical Society B 41(2): 276–278.
- Tank, F. and Tuncel, A. (2015). Some results on the extreme distributions of surplus process with nonhomogeneous claim occurrences, Hacettepe Journal of Mathematics and Statistics 44(2): 475–484.
- Tremblay, L. (1992). Using the Poisson inverse Gaussian in bonus-malus systems, Astin Bulletin 22(1): 97–106.
- Tzougas, G., Hoon, W. and Lim, J. (2019a). The negative binomial-inverse Gaussian regression model with an application to insurance ratemaking, European Actuarial Journal 9(1): 323–344.
- Tzougas, G., Yik, W. and Mustaqeem, M. (2019b). Insurance ratemaking using the exponential-lognormal regression model, Annals of Actuarial Science 14(1): 42–71.
- Walhin, J. and Paris, J. (1999). Using mixed Poisson processes in connection with bonus-malus systems, ASTIN Bulletin 29(1): 81–99.
- Willmot, G. (1986). Mixed compound Poisson distributions, ASTIN Bulletin 16(1): 59–79.
Language: English
Page range: 637 - 650
Submitted on: Jun 10, 2023
Accepted on: Sep 11, 2023
Published on: Dec 21, 2023
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
Keywords:
Related subjects:
© 2023 Weenakorn Ieosanurak, Banphatree Khomkham, Adisak Moumeesri, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.