Copula-based dependence between frequency and class in car insurance with excess zeros

A bonus-malus system calculates the premiums for car insurance based on the previous claim experience (class). In this paper, we propose a model that allows dependence between the claim frequency and the class occupied by the insured using a copula function. It also takes into account zero-excess phenomenon. The maximum likelihood method is employed to estimate the model parameters. A small simulation is performed to illustrate the proposed model and method.