相依风险的团体健康保险损失预测  

Loss Prediction of Group Health Insurance with Dependent Risks

作　　者：李政宵 孟生旺[2,3,4] LI Zheng-xiao1, MENG Sheng-wang2,3,4(1. School of Insurance and Economics, University of International Business and Economics, Beijing 100029, China; 2. Center for Applied Statistics, Renmin University of China, Beijing 100872, China; 3. School of Statistics, Renmin University of China, Beijing 100872, China; 4. School of Statistics, LanZhou University of Finance and Economics, Gansu Lanzhou 730101, Chin)

机构地区：[1]对外经济贸易大学保险学院,北京100029 [2]中国人民大学应用统计科学研究中心,北京100872 [3]中国人民大学统计学院,北京100872 [4]兰州财经大学统计学院,甘肃兰州730101

出　　处：《数理统计与管理》2018年第3期399-412,共14页Journal of Applied Statistics and Management

基　　金：教育部人文社会科学重点研究基地重大项目(16JJD910001);国家社科基金重大项目(16ZDA052)

摘　　要：在团体健康保险中，同一份保单通常包含若干被保险人，被保险人之间相依的风险特征使得保单的赔付数据呈现出分层结构的特点。同时，保单的索赔次数和索赔强度通常存在一定的相依关系，这种相依关系对保险公司纯保费的厘定结果具有重要的影响。为了准确预测团体健康保险的纯保费，本文建立了相依风险的贝叶斯分层模型，该模型用伽马分布来描述索赔强度数据，用零截断泊松分布来描述索赔次数数据，分别在模型均值中引入共同的随机效应来描述赔付数据的分层特征和索赔次数与索赔强度之间的相依关系；最后借助贝叶斯HMC算法进行参数估计，并给出了团体保单的损失预测分布。本文将该方法运用到我国一组团体健康保险的损失数据并对保单累积损失进行预测。结果表明，相依风险的贝叶斯分层模型具有良好的应用价值。In the group health insurance, the policy usually contains several insureds. As the group insureds share similar risk characteristics, the claim data shows the hierarchical feature. Considering the dependence between numbers of claim and claim severity, this paper presents a Bayesian hierarchical model to predict the total loss. This model first assumes the numbers of claim follow the zero-truncated Poisson distribution and claim severity follows the gamma distribution, and then introduces the common random effect into the model to taking into account both the dependence between claim numbers and claim severity and the hierarchical structure of claim data. Finally, Bayesian approach is used to estimate the parameters and derive the predictive distribution of total loss. Numerical analysis is performed with claim data of the group health insurance from an insurance company, and the result shows that the model is appropriate to predict the total loss.

关 键 词：贝叶斯分层模型 相依关系 共同随机效应 团体健康保险 

分 类 号：F222.3[经济管理—国民经济] O212[理学—概率论与数理统计]