Experience Bayesian Estimate Of Liability Reserve In Stochastic B-F Model

In the B-F reserve model,the estimations of accident year mean are very critical.However,the traditional approach assume that there are some prior estimates for accident year means which are determined by the actuary based on past experience,which has great subjectivity.If the prior estimates are chosen correctly,we will get an accurate estimate of the reserve.On the contrary,if the prior estimate are selected incorrectly,there must be bring large errors in the reserve estimates.In Chapter 3 of this paper,we present an improved stochastic B-F reserve model.The ideas from credibility theory are used and the credibility estimates of accident year means are derived.In addition,the empirical Bayes approach are investigated and the estimations of structural parameters are given.Furthermore,we get empirical Bayes estimates of reserves.We use numerical simulation to verify the mean square error for Empirical Bayes estimates,and the conclusions show that this empirical Bayes estimates are valid in stochastic B-F model.In chapter4,the stochastic B-F model is further extended.The variance structure of the incremental claim is assumed to follow B(?)hlmann-Straub model which is the same as credibility model.The optimal linear estimate of claim mean is derived in stochastic B-F model.The estimation of the structural parameters is also given,and some statistical properties of the estimation are proved.In addition,practical examples of insurance company are given and the differences are compared among our empirical Bayes estimates obtained,chain ladder estimates and traditional B-F estimates.Finally,the whole paper is summarized and the directions of further improvement are suggested.