广义线性混合模型及其在非寿险信度费率厘定中的应用  

Generalized Linear Mixed Models and Its Application in Non-life Insurance Credibility Rates

作　　者：康萌萌 

机构地区：[1]山东财经大学保险学院,山东济南250014

出　　处：《统计与信息论坛》2018年第1期72-78,共7页Journal of Statistics and Information

基　　金：国家社会科学基金<波动率不确定情形下的动态风险度量及期权定价研究>项目资助(15BJY007);国家自然科学基金<保险风险的随机建模分析与优化控制策略研究>项目资助(11301303);山东省泰山学者工程专项经费资助(tsqn20161041)

摘　　要：近年来,国内外精算学者开始将广义线性混合模型用于信度模型费率厘定中,但他们对因变量的推广仅仅推广到负二项分布。在前人的研究基础上,将因变量进一步推广到负二项K、广义泊松、双泊松等分布,然后用极大似然估计中的限制性虚拟似然法和自适应高斯求积法对参数进行估计,最后用美国劳工补偿保险进行实证分析。结果表明:负二项K(K=1.947)广义线性混合模型对数据拟合效果最好,其次为负二项1、负二项2、双泊松、广义泊松和泊松广义线性混合模型。Credibility theory is a common pricing method in non-life insurance.In recent years,scholars at home and abroad have begun to apply the generalized linear mixed model to the credibility model pricing.But there is a problem in their study,the dependent variable only extended to negative binomial distribution.On the basis of previous research,the dependent variable is extended to negative binomial distribution K distribution,generalized Poisson,double Poisson distribution,then using(Restricted)Pseudo-likelihood method and(Adaptive)Gauss-Hermite quadrature method to estimate the parameters,finally empirical analysis the labor compensation insurance,comparing the model fitting effect and obtaining optimal model.

关 键 词：广义线性混合模型 信度理论 负二项分布 

分 类 号：F840[经济管理—保险]