随机B-F准备金模型中事故年索赔均值的信度估计  

The Credibility Estimation of Accident Year Mean in the Model of Stochastic B-F Reserve

作　　者：章溢[1,2] 温利民[1] 王江峰[3] 王伟[4] 

机构地区：[1]江西师范大学数学与信息科学学院,南昌330022 [2]江西师范大学计算机信息工程学院,南昌330022 [3]浙江工商大学统计系,杭州310018 [4]宁波大学理学院,宁波315211

出　　处：《应用数学学报》2016年第2期306-320,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.71361015);江西省自然科学基金(No.20142BAB201013);教育部人文社科基金(No.15YJC910010,15YJC910006);浙江省教育厅科研项目(No.Y201534425)资助

摘　　要：在B-F准备金模型中,事故年均值的估计是一个非常关键的估计量,然而传统的做法是假定事故年均值存在某个先验估计,这个先验估计是根据以往的经验资料由精算师确定的,具有很大的主观性.若先验估计选择合适,则能得到准备金的准确估计,反之,若先验估计选取错误,则给准备金估计带来较大的误差.本文提出改进的随机B-F准备金模型,利用信度理论的思想给出事故年随机索赔均值的信度估计,进而利用经验贝叶斯的方法得到了先验分布中结构参数的估计,最后得到责任准备金的经验贝叶斯估计.我们利用数值模拟的方法验证了事故年均值的经验贝叶斯的均方误差.结论显示,这种随机B-F模型的经验贝叶斯估计是有效的.最后,给出保险公司的实际例子,将本文得到的准备金经验贝叶斯估计与传统的B-F估计和链梯法估计进行了比较.In the B-F reserve model, the estimations of accident year mean are very crit- ical in reserve model. 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 choose correctly, we will get the an accurate estimate of the reserve. On the contrary, if the a prior estimate are selected incorrectly, there must be bring large errors in the reserve estimates. This paper presents 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. Further- more, 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. Finally, practical examples of insurance company are given and the differences are compared among our empirical Bayes estimates obtained, chain ladder estimates and traditional BF estimates.

关 键 词：准备金 B-F模型 信度估计 链梯法 经验贝叶斯估计 

分 类 号：O211.9[理学—概率论与数理统计]