Multivariate Credibility in Bonus-Malus Systems Distinguishing between Different Types of Claims

Emilio Gómez-Déniz and Enrique Calderín-Ojeda
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Emilio Gómez-Déniz: Department of Department of Quantitative Methods, Faculty of Economics and Business Sciences, TiDES Institute, University of Las Palmas de Gran Canaria, Canary Islands, E-35017 Las Palmas de Gran Canaria, Spain
Enrique Calderín-Ojeda: Centre for Actuarial Studies, Department of Economics, University of Melbourne, Melbourne VIC 3010, Australia

Risks, 2018, vol. 6, issue 2, 1-11

Abstract: In the classical bonus-malus system the premium assigned to each policyholder is based only on the number of claims made without having into account the claims size. Thus, a policyholder who has declared a claim that results in a relatively small loss is penalised to the same extent as one who has declared a more expensive claim. Of course, this is seen unfair by many policyholders. In this paper, we study the factors that affect the number of claims in car insurance by using a trivariate discrete distribution. This approach allows us to discern between three types of claims depending wether the claims are above, between or below certain thresholds. Therefore, this model implements the two fundamental random variables in this scenario, the number of claims as well as the amount associated with them. In addition, we introduce a trivariate prior distribution conjugated with this discrete distribution that produce credibility bonus-malus premiums that satisfy appropriate traditional transition rules. A practical example based on real data is shown to examine the differences with respect to the premiums obtained under the traditional system of tarification.

Keywords: Bayesian; bonus-malus system; claim number; claim size; conjugate distribution (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2018
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