Modelling of Multivariate Loss Reserving with Contaminated GeneralizedBeta Type-II Margins Using Copulas

In this paper, we consider the loss reserving problem based on a portfolio of dependent run-off triangles. We propose to use copula to capture the dependence among triangles. For each triangle, we employ the contaminated generalized beta type II, a heavy tailed distribution, to model the marginal distribution of the loss payments in each triangle. We use the copulas Clayton, Frank, Gumbel and Gaussian and the ANOVA and ANCOVA models for the mean function. We apply the proposed models to the data set that consists of two lines of business (personal and commercial auto lines) of paid losses data from the Schedule P of the National Association of Insurance Commissioners (NAIC) database. Based on a Bayesian data analysis, we find that the ANOVA model with the Gaussian copula admits the best fitting performance. The ANCOVA model with the Clayton copula has the best performance in terms of prediction accuracy.