Abstract
A comprehensive auto insurance policy usually provides the broadest protection for the most common events for which the policyholder would file a claim. On the other hand, some insurers offer extended third-party car insurance to adapt to the personal needs of every policyholder. The extra coverage includes cover against fire, natural hazards, theft, windscreen repair, and legal expenses, among some other coverages that apply to specific events that may cause damage to the insured’s vehicle. In this paper, a multivariate distribution, based on a conditional specification, is proposed to account for different numbers of claims for different coverages. Then, the premium is computed for each type of coverage separately rather than for the total claims number. Closed-form expressions are given for moments and cross-moments, parameter estimates, and for a priori premiums when different premiums principles are considered. In addition, the severity of claims can be incorporated into this multivariate model to derive multivariate claims’ severity distributions. The model is extended by developing a zero-inflated version. Regression models for both multivariate families are derived. These models are used to fit a real auto insurance portfolio that includes five types of coverage. Our findings show that some specific covariates are statistically significant in some coverages, yet they are not so for others.
Highlights
In the automobile insurance sector, it is natural to calculate the a priori premium taking into account the number of claims and individual characteristics of each insured, such as gender, age, years of validity of the policy, etc
This procedure to compute the a priori premium is usually completed via parametric models rather than using the ordinary regression model, which can predict values of the number of claims even if negative
J=2 Θ ji = 1, i.e., every claim in coverage j is a proportion of the total claims N1i
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The purpose of this paper is to introduce a novel methodology based on a multivariate distribution via a conditional specification, proposed to account for different numbers of claims in different coverages and for the total claims frequency This approach enable us to examine the dependence structure of a finite number of coverages in motor vehicle insurance and incorporate heterogeneity in the model through explanatory variables. We use this procedure to calculate premiums based only on the claims frequency.
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