| In this paper,we study two bivariate bonus-malus systems,based on theoretical assumptions of the number of claims(binomial distribution and negative binomial distribution),considering the size of claim amount.We introduce a covariate according to the size of claims,then use the prior distribution and the likelihood function to construct two Bayesian models.The corresponding Bayesian premiums and bonus-malus coefficients are derived by theoretical derivation.And the maximum likelihood estimation of the parameters in the model based on the zero-inflated geometric distribution is discussed.In the numerical experiment,the Bayesian model based on negative binomial distribution is used to fit a real data set.The result shows that bonus-malus coefficients of the model can reasonably reflect the policyholder’s risk level,which means,the higher risk level,the bigger bonus-malus coefficient.In addition,it is necessary to choose a reasonable claim threshold,which will affect the rewarding and punishing strength of the model. |
