失真风险保费的最优经验厘定  

Optimal Experience Rating of Distortion Risk Premiums

作　　者：章溢[1,2] 李志龙 龚海林[1] 温利民[1] ZHANG Yi;LI Zhilong;GONG Hailin;WEN Limi(School of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022,China;School of Statistics,Jiangxi University of Finance and Economics,Nanchang 330013,China)

机构地区：[1]江西师范大学数学与信息科学学院,南昌330022 [2]江西财经大学统计学院,南昌330013

出　　处：《应用数学学报》2019年第6期761-778,共18页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(71761019);江西省自然科学基金(20171ACB21022);江西省研究生创新基金(YC2018-B059)资助项目

摘　　要：研究了贝叶斯模型中失真风险保费的经验厘定问题.通过弓I入分布函数的加权积分损失函数,利用信度理论的方法最小化期望损失得到分布函数的最优线性估计,进而得到失真风险保费的两个信度估计,并对信度估计的统计性质进行了比较.文章还讨论了失真函数和权重函数的选取问题,给出了结构参数的估计方法,证明了估计的无偏性和相合性.最后,利用数值模拟的方法验证了估计的收敛情况,并对不同失真函数下的收敛情况进行了比较.The experience rating of the distortion risk premium in Bayesian models is studied.By introducing the weighted integral loss function of distribution function and using thecredibility theory method, the optimal linear estimation of distribution function is obtainedby minimizing the expected loss, and the two credibility estimators of the distortion riskpremium are obtained, and the corresponding statistical properties of the two estimator arecompared. The article also discusses the selection of the distoTtion function and the weightfunc tion. The met hod of estimating the struc ture parame tets is given and the unbiasednessand consistency of the estimation are proved. Finally, the numerical simulation is used toverify and compare the convergence rate under different distortion functions.

关 键 词：失真保费原理 风险保费 经验厘定 相合性 

分 类 号：O212.9[理学—概率论与数理统计]