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Design of Optimal Bonus-Malus Systems With a Frequency and a Severity Component On an Individual Basis in Automobile Insurance

Published online by Cambridge University Press:  29 August 2014

Nicholas E. Frangos  and
Spyridon D. Vrontos
Nicholas E. Frangos
Affiliation:
Department of Statistics, Athens University of Economics and Business, Patission 76, 10434, Athens, Greece, E-mail:[email protected] and [email protected]
Spyridon D. Vrontos
Affiliation:
Department of Statistics, Athens University of Economics and Business, Patission 76, 10434, Athens, Greece, E-mail:[email protected] and [email protected]
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Abstract

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The majority of optimal Bonus-Malus Systems (BMS) presented up to now in the actuarial literature assign to each policyholder a premium based on the number of his accidents. In this way a policyholder who had an accident with a small size of loss is penalized unfairly in the same way with a policyholder who had an accident with a big size of loss. Motivated by this, we develop in this paper, the design of optimal BMS with both a frequency and a severity component. The optimal BMS designed are based both on the number of accidents of each policyholder and on the size of loss (severity) for each accident incurred. Optimality is obtained by minimizing the insurer's risk. Furthermore we incorporate in the above design of optimal BMS the important a priori information we have for each policyholder. Thus we propose a generalised BMS that takes into consideration simultaneously the individual's characteristics, the number of his accidents and the exact level of severity for each accident.

Keywords

Optimal BMSclaim frequencyclaim severityquadratic loss functiona priori classification criteriaa posteriori classification criteria
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 31 , Issue 1 , May 2001 , pp. 1 - 22
Copyright
Copyright © International Actuarial Association 2001

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