The UMVUE Of The IBNR

Accurate estimation of the level of the Outstanding Claims Reserve for an insur ance company is required because it is the major liability in insurance company's balance sheet and it impacts on multiple aspects of the operation of the insurance company:dividend declaration, solvency, insurance product pricing and tax payments.Use the present method which based on Chain-Ladder method to es-timate the IBNR in insurance practice we could only get the value of the estimate, and the properties only unbiased and so on, but the variance of the estimation is barely researched. Based on the Professor Zhongxian Han,Wu-Chyuan Gau's idea of estimating the estimation of the Outstand-ing Claims Reserve, we obtain the uniformly minimum variance unbiased estimatior(UMVUE) of the Outstanding Claims Reserve and it's variance's UMVUE.Firstly we present some methods which are frequently-used to estimate the Outstanding Claims Reserve, especially emphasis introduce the Chain-Ladder method, and then compare them. Then apply the lognormal regres-sion to the Chain-Ladder method to obtain the UMVUE of the Outstanding Claims Reserve. Finally we prove the variance of the reserve which is ob-tained from the model in this article is the smallest by an example.Furthermore, the proposed method can be applied to the BF method, and the standard error of BF reserves can be quantified, the accuracy of the estimation can be raised, the information of the error of the estimation can be obtained. The insurance corporation could use these information to estimate the reserve and lower the risk on business operation.