## Copula-based dependence between frequency and class in car insurance with excess zeros.(English)Zbl 1408.91110

Summary: 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.

### MSC:

 91B30 Risk theory, insurance (MSC2010) 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62P05 Applications of statistics to actuarial sciences and financial mathematics

### Keywords:

car insurance; bonus-malus; dependent; zero-inflated; copula function
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### References:

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