Multivariate Zero-Inflated Inar(1) Model with an Application in Automobile Insurance

The aim of this paper is to propose a multivariate INAR(1) model for addressing all the challenges in high-dimensional non-life claim count data sets that exhibit time and cross dependence and a zero-inflation attribute. In particular, the innovation terms are modelled using a multivariate zero-inflated Poisson distribution or a multivariate zero-inflated hurdle Poisson distribution which can handle extra zeros in the data. Furthermore, the proposed modelling framework can take into account the influence of individual and coverage-specific covariates on the mean parameters of each model which enables the calculation of tailored made insurance premiums according to different risk profiles. Maximum likelihood estimation of the model parameters is achieved through a novel Expectation-Maximization algorithm which is demonstrated to perform satisfactorily when we exemplify our approach on the European Motor Third Party Liability claim count data