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OPTIMAL BONUS-MALUS SYSTEMS USING FINITE MIXTURE MODELS

Published online by Cambridge University Press:  10 January 2014

George Tzougas ,
Spyridon Vrontos  and
Nicholas Frangos
George Tzougas
Affiliation:
Department of Statistics, Athens University of Economics and Business, Athens, Attica, Greece
Spyridon Vrontos
Affiliation:
Department of Accounting, Finance and Governance, University of Westminster, London, UK, Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Attica, Greece
Nicholas Frangos*
Affiliation:
Department of Statistics, Athens University of Economics and Business, 76 Patission Street, Athens 10434, Attica, Greece, Tel: +302108203579
*
E-Mail: [email protected]
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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.

Keywords

Optimal BMSclaim frequencyclaim severitymixtures of distributionsa priori classification criteriaa posteriori classification criteria
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 44 , Issue 2 , May 2014 , pp. 417 - 444
Copyright
Copyright © ASTIN Bulletin 2014 

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