Modified pseudo-copula regression model

In non-life insurance calculations, the assumption that the claim severity and frequency are independent is frequently used. Although the independence assumption greatly simplifies many of the calculations, it is not very realistic, and it can often lead to over or under estimation of quantities of interest. For this reason, the dependency should be modeled and included in the calculations instead of the independence assumption. In this thesis, it is aimed to analyse and model the dependency between the claim severity and frequency in non-life insurance. For this purpose, the claim severity and the claim frequency are modeled with marginal gamma and marginal Poisson generalized linear models, respectively. By considering these generalized linear models together with the modified pseudo-Gauss copula functions, the modified pseudo-copula regression model is proposed. With the pseudo-copulas, close estimations to the real data are found, and with the modified correlation coefficients, a flexible dependency modeling is presented according to the dependency between the claim severity and frequency. The proposed model is tested with both simulation and real data analysis. The efficiency of the modification on the pseudo-copula function is analyzed under different scenarios with the simulation study. In the real data analysis, in insurance portfolios where there is different relationships between claim severity and frequency, the dependency between the claim severity and frequency is modeled with the modified pseudo-copula regression model. The pseudo-maximization by parts method is used in the parameter estimation. Under the assumption of independence and when dependency is taken into account, the mean square errors of the parameter estimates according to different modifications are calculated and compared. It is observed that the parameters estimated by the modified pseudo-copula regression model have lower mean square error than the estimates found with the model using the constant correlation coefficient and the model under the independence assumption. Finally, the standard copula regression model and the modified pseudo-copula regression model are compared and it is observed that the proposed model give better results.