The Application Of Relevant Bayesian Model In The Non-life Insurance Reserves

With Bayesian methods in the study of outstanding claims reserve in a wide range of applications, and a variety of statistical software development, the current application of Bayesian methods have a lot of improvements, such as considering the traffic triangle in the case of negative, discussing the introduction of robustness and correlation of the Bayesian methods, the present of the Bayesian hierarchical theory and so on. De Alba and Neito-Barajas(2008) proposed a relevant Bayesian model, this model to describe the correlation between the development years by constructing a relevant Gamma process. Based on the research of De Alba and Neito-Barajas,in this article, we will extend the relevant Gamma process to a more general case. We propose two relevant processes based on the distribution of beta family and the distribution of closed convolution exponential family, the process will be extended to the relevant Gamma more general correlation process is proposed based on the relevant. In third Chapter, we describe the relevant Bayesian method in detail to estimate outstanding claims reserve model.Bayesian model parameter estimation is more complex, you can usually use a computer numerically solved. There are common methods Markov chain Monte Carlo(MCMC method),and in which the most widely used is Gibbs sampling method. In this paper, the empirical research has used the Gibbs sampling method, then obtained parameter estimates by R and BUGS software programming, and further obtain the reserve.Finally, the improved model was applied in empirical research, and through the R and BUGS software programming, we use numerical algorithm to estimate the parameters. By comparing the independent Bayesian models and associated Bayesian model results, it shows that this relevant Bayesian model is more reasonable than the traditional independent Bayesian model.