A modified pseudo-copula regression model for risk groups with various dependency levels

Abstract

In this study, the modified pseudo-Gaussian copula function is considered together with marginal gamma and Poisson generalized linear models and a modified pseudo-copula regression model is proposed to model dependency between claim severity and frequency. With the pseudo-copula, close estimates to the real values were found, and flexible dependency modelling is presented with the modified correlation coefficients according to the dependence between the claim severity and frequency of different risk groups. The pseudo-maximization by parts method was used for parameter estimation by developing the maximization by parts algorithm. The proposed model was analyzed with both simulation and real data analysis. Under the assumption of independence and when dependency is taken into account, the mean square errors of the parameter estimates according to different modifications were calculated and compared. The parameters estimated by the modified pseudo-copula regression model have lower errors than the estimates found using the model with fixed correlation coefficient and the model under the independence assumption. Finally, the models were compared and it was observed that the proposed model gives better results.