The Credibility Prediction For Liability Reserve Under The Linear Bayesian Model

Reserve of the non-life insurance is the main liabilities for insurance company. The adequacy of reserve constitutes an important basis of the insurance company’s ability to fulfill the insurance liability and the accuracy of reserve is the basis of operating cost. The assessment of non-life insurance reserve has been a hot and difficult problem both in actuarial theory and application aspects at home and abroad. The traditional evaluation model of liability reserves include chain ladder and BF method, most of which only use claims sample information, but seldom consider to use the priori information. In this paper, we will establish bayesian model of liability reserves which axe based on prior information and make liability reserves predictions with linear bayesian methods. At first introduces the background of liability reserve and the assessment methods of traditional reserve. Then describes the general bayesian model and obtains liability reserve assessment under the assumption of the prior distribution and the sample distribution. we establish bayesian model to the incremental claims and use the linear bayesian methods to get the credibility estimation of liability. We also make use of bayesian techniques to build empirical bayes model of liability reserve, thus the estimates that we have already got wouldn’t depend on any structural parameter and can be directly applied.In order to consider covariance information,We establishes linear random effects model, and gets the final estimate of claims by using linear bayesian methods again, then discusses the properties of estimationt. At last, we verify the effects of the estimation by numerical simulation. The fifth chapter establishes a multidimensional bayesian models to multiple claims triangle data, and discusses liability reserve estimate vector by using linear bayesian methods of random vector. This model can handle the issue of liability reserve funds that have dependent situation in claims. The sixth chapter is a summary of the full text and proposes directions for further research.