Research On Non-life Insurance Multivariate Claims Reserve Evaluation Methods Based On The Copula Function

Non-life insurance claims reserve evaluation methods are the important part in the balance sheet of Non-life insurance companies, and they are also a kind of evaluation strategy for China association of insurance supervision and administration to supervising the Non-life insurance companies. The method of assess claims reserve divides into the univariate claim reserve evaluation methods and the multivariate claim reserve evaluation methods, the univariate claim reserve evaluation methods are the traditional method, they has already formed a kind of fixed system in practical operation. Thus, the current research emphasizes the multivariate claim reserve evaluation methods. While in the field of the probability theory, the copula function is the more practical function to explaining the multivariate correlation. It is used for the field of the financial stocks and analyzes or estimates the correlation between the development trend of the different stocks or the financial asset variables. Based on the above background and the multivariate claim reserve evaluation method, the article has improved for the multivariate preparation progress method and the multivariate munch chain ladder method.Based on deterministic reserve progress method, the reserve progress method joins the random factors of variable, then it turns into the randomness reserve progress method. On the base of the randomness reserve progress method, the article gets through the copula function to estimating the correlation between variables which have randomness, and it combines the unique characteristic of the copula function with the reserve progress method. In the same way,the chain ladder method is also a traditional univariate claim reserve evaluation method,it has ordinal optimized for the munch chain ladder method and the randomness munch chain ladder method on the basis of the predecessors. First of all, the article takes advantage of the nonparametric kernel density method to estimates the copula function between variables, then on the basis of the randomness munch chain ladder method, it explains the relevance by using the copula function which is estimated to optimizing and improving the randomness munch chain ladder method. In the part of instance analysis, the article selects the run-off triangle of the total paid reparations and the run-off triangle of the total reported reparations which have representative in Non-life insurance theory research. For the multivariate claim reserve evaluation method, it calculates and compares the mean square error of prediction andpredictive distribution of outstanding claims reserves in the deterministic reserve progress method, the random reserve progress method and the multivariate preparation progress method which is based on the copula function. Similarly, for the multivariate munch chain ladder method, it compares the predictive distribution and the mean square error of prediction of outstanding loss reserve in the munch chain ladder method, the randomness munch chain ladder method and the multivariate munch chain ladder method which is based on the copula function. Applying the Matlab which is mathematical software and the bootstrap method, it is comparative results to drawing the conclusion that the mean square error of prediction for the multivariate preparation progress method which is based on the copula function is smaller than the random reserve progress method, and the mean square error of prediction for the multivariate munch chain ladder method which is based on the copula function is smaller than the munch chain ladder method or the randomness munch chain ladder method. Thus it illustrates the effectiveness for introducing the copula function.