链梯法中进展因子估计的数学规划法  

Estimate the Development Factor of Chain-Ladder Method by Using Mathematical Programming

作　　者：卢志义[1] 刘乐平[2] 张慧[1] 

机构地区：[1]天津商业大学理学院,天津300134 [2]天津财经大学统计系,天津300222

出　　处：《数学的实践与认识》2015年第5期249-255,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71371138;71171139);全国统计科学研究计划项目(2012LY107);天津市高等学校科技发展基金计划项目(20121004)

摘　　要：对传统链梯法中进展因子估计方法的不足进行了简要分析,提出将两种形式的偏差函数作为目标函数,建立二次规划和目标规划模型对进展因子进行估计.同时,对不同事故年赋予不同的权重因子,以区别不同数据信息在进展因子估计中的作用,弱化异常数据对进展因子估计的影响.通过数值实验对所述方法的可行性进行验证.The drawbacks of the traditional Chain-ladder technique are analyzed briefly. Two types of deviation function which will be taken as the object function are proposed. Quadratic programming and objective program＇ming are established to estimate development factor. Meanwhile, weight of each accident year is proposed to distinguish the action of different data and to abate the influence of the singularity in the estimate of the development factor. An example is shown to illustrate the availability of the methods.

关 键 词：链梯法 进展因子 二次规划 目标规划 

分 类 号：O221[理学—运筹学与控制论]