Using Convex Combination Of Copula And EM Algorithm For Credibility

In this paper, using longitudinal data, we develop the theory of credibility by copula model. Instead of a single copula, the convex combination of copulas is used to describe the dependencies among claims. And we use EM algorithm to overcome the problem generated by incomplete data. For the marginal claims distributions, we use generalized linear models. Finally, for comparing with the results of a single copula, using EM algorithm, some simulations of Massachusetts automobile claims are presented.This dissertation is organized as follows:In chapter1, we introduce the background of the research and relative definitions and properties.In chapter2, we introduce that how to model credibility by the convex combination of copulas and how to use EM algorithm to estimate parameters by incomplete-dataIn chapter3, we discuss parameter estimation. Using Maximum Likelihood method, the results of three models are given for the comparison respectively in this section.In the end, we come to the conclusion.