Abstract
In this paper, a flexible count regression model based on a bivariate compound Poisson distribution is introduced in order to distinguish between different types of claims according to the claim size. Furthermore, it allows us to analyse the factors that affect the number of claims above and below a given claim size threshold in an automobile insurance portfolio. Relevant properties of this model are given. Next, a mixed regression model is derived to compute credibility bonus-malus premiums based on the individual claim size and other risk factors such as gender, type of vehicle, driving area, or age of the vehicle. Results are illustrated by using a well-known automobile insurance portfolio dataset.
Highlights
A modification in the bonus-malus systems was proposed Gómez-Déniz (2016), which are commonly applied in automobile insurance, that differentiated between two different types of claims by including a bivariate model based on the assumption of dependence
The aforementioned work studied the impact on the bonus-malus premium in a general setting without involving individual’s risk factors, such as gender, type of vehicle, area of circulation, etc
An extensive set of a priori classification variables such as age, gender, type and age of car, etc., will be used to incorporate, depending on the heterogeneity of the insured’s behaviour, prior distributions assigned to the parameters of the model to build up a posteriori credibility, bonus-malus premiums
Summary
A modification in the bonus-malus systems was proposed Gómez-Déniz (2016), which are commonly applied in automobile insurance, that differentiated between two different types of claims by including a bivariate model based on the assumption of dependence. In the mentioned work a bivariate prior model, conjugated with respect to the likelihood, was proposed, and as a result of this, simple credibility bonus-malus premiums that satisfy appropriate transition rules were obtained. These expressions were used to compute credibility bonus-malus premiums by considering two different types of claims: those ones above and below a threshold claim size, say ψ > 0. An extensive set of a priori classification variables such as age, gender, type and age of car, etc., will be used to incorporate, depending on the heterogeneity of the insured’s behaviour, prior distributions assigned to the parameters of the model to build up a posteriori credibility, bonus-malus premiums. Numerical illustrations and results connected with the compound model are shown in Section 5, and Section 6 concludes the work
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