准备金评估的贝叶斯分层分位回归模型  

Assessment of outstanding reserving based on bayesian hierarchical quantile regression

作　　者：杨亮[1,2] 孟生旺 Yang Liang;Meng Shengwang(School of Statistics,Renmin University of China,Beijing 100872,China;School of Insurance,Southwest University of Finance and Economics,Chengdu 611130,China;Center for Applied Statistics,Renmin University of China,Beijing 100872,China)

机构地区：[1]中国人民大学统计学院,北京100872 [2]西南财经大学保险学院,四川成都611130 [3]中国人民大学应用统计科学研究中心,北京100872

出　　处：《系统工程学报》2019年第5期672-682,共11页Journal of Systems Engineering

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

摘　　要：基于AL(asymmetric Laplace)分布建立了贝叶斯分层参数化分位回归模型,并与传统的非参数化分位回归模型进行了比较.通过蒙特卡洛方法从参数的后验分布中反复抽样,借助分位函数的表达式,获得了准备金风险边际的分布,进而给出了风险边际的置信区间.基于一组增量赔款数据的分析结果表明,贝叶斯分层参数化分位回归模型可显著改善传统分位回归模型对未决赔款准备金的预测效果,并为保险公司的风险管理提供更多有价值的信息.Based on the asymmetric Laplace(AL) distribution, a Bayesian hierarchical parametric quantile regression model is established to compare with the traditional nonparametric quantile regression models. By using Monte Carlo method, samples are drawn from the posterior distribution of parameters, and the distribution and confidence interval of the risk margin are established using expressions of the quantile function. An analysis based on a set of incremental claims data shows that the Bayesian hierarchical parametric quantile regression model can significantly improve the forecasting of non-life loss reserving, and can provide more valuable information for risk management of insurance companies.

关 键 词：非寿险 未决赔款准备金 分位回归 非对称拉普拉斯分布 

分 类 号：O212[理学—概率论与数理统计]