新型广义加权保费原理下风险保费的信度估计  

The Credibility Estimators of Risk Premium Under a New Type of Generalized Weighted Premium Principle

作　　者：温利民[1,2] 梅国平[1,3] 

机构地区：[1]江西师范大学数信学院,南昌330022 [2]江西财经大学博士后流动站,南昌330013 [3]江西财经大学信息管理学院,南昌330013

出　　处：《应用数学学报》2013年第2期257-268,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(71001046;71071056;71063006);江西省自然科学基金(20114BAB211004)资助项目

摘　　要：本文研究了新型广义加权保费原理下风险保费的信度估计问题.利用了损失函数法,将新型广义加权保费原理定义为新型广义加权损失函数下风险的最优估计.在该损失函数下,把估计限定在经验估计的线性组合,根据均方误差最小原则得到风险保费的信度估计,并证明了信度估计的相合性.最后,在Esscher保费原理下对信度估计的相合性进行模拟验证,并在指数保费原理下与前人的结果进行了比较,结果发现已有的研究只是本文的一种特殊情况.In this paper, we study the credibility estimator of risk premium under the new-type generalized weighted premium principle. Use of a loss function method, the new generalized weighted premium principle is defined as the optimal estimate of the risk under the new-type generalized weighted loss function. Under this type of loss function, we con- strain the estimator of risk premium to linear combination of empirical estimate and derive the credibility estimator of risk premium by minimizing the mean square error. We also prove the consistency of the credibility estimator. Finally, the numerical example is given under Esscher principle to verify the results of the paper. In addition, we also compare the credibility estimator under exponential principle with previous research. The results show that the previous estimator is the special case of this paper.

关 键 词：新型广义加权保费原理 风险保费 信度估计 BAYES估计 相合性 

分 类 号：O211.9[理学—概率论与数理统计]