Based On Copula Multivariate Reserving For Outstanding Losses

In the field of non life insurance actuarial, people mainly focus on the estimation of single business reserve. When in the non life insurance company assess the level of the total reserves of all operations, because there is a certain correlation between the different business, total reserves for the simple addition of a single business reserve are often greater than the actual amount of claims. Therefore, it is necessary for us to study the outstanding claims reserve of multi service.A method of multiple claims reserve is using multiple chain ladder model and multiple additive model, but this is Copula connection function. It is a one-dimensional model of loss variables on a single business as a marginal distribution, recanalization over Copula function to establish a multi-dimensional joint distribution model of the multi service claims variables, so as to investigate the total portfolio of outstanding claims reserve.The multivariate normal Copula model analyzes the transformed variables using fac-tor analysis. R software is applied to estimate the models using two-stage maximum likelihood estimation method, which uses known data to estimate the marginal distribu-tion of the related parameters, and then further estimates the related parameters of copula model by the known quantity. The end, by the method of stochastic simulation we get the future of the business of the incremental compensation, and then calculate the total outstanding claims reserve.In order to better compound market "the peak, thick tail, skew characteristics", we propose a multivariate t-Copula model and a mixing normal-normal inverse Gaussian (G-NIG) Copula model. We get the future of the business of the incremental compensation by using model construction, factor analysis method and software R stochastic simulation before.The size of the coefficient of variation can be explained by the stability of the model, while the decline in the risk margin be explained by the need for the study of the relevant issues in the estimation of the total reserves. So we compare the three models from the stability and ease of operation.