《保险研究》20190307-《高龄人口死亡率预测模型的比较与选择》（王晓军、路倩）

［摘   要］高龄人口死亡率预测模型是人口预测、养老金成本和债务评估以及长寿风险度量与管理的基础。我国大陆地区高龄人口死亡数据量少、数据波动性大,如何选择适合我国高龄数据特点的死亡率预测模型,是重要的研究课题。本文在归纳总结死亡率预测模型研究进展的基础上,先采用数据较为充分的台湾地区高龄死亡数据,选用Lee-Carter、CBD、贝叶斯分层模型等八种死亡率模型,对模型的拟合效果、预测效果和稳健性做出比较。在此基础上,基于修正和平滑后的我国大陆人口死亡数据,采用CBD模型和贝叶斯分层模型建模和预测。结果显示:贝叶斯分层模型能捕捉我国大陆高龄死亡率数据的历史波动,预测区间能够涵盖全部死亡率的真实值,但预测区间过宽,生存曲线不收敛；相比之下,CBD模型对我国大陆地区高龄死亡率的拟合和预测较好,预测区间和生存曲线合理。在长寿风险度量中,建议采用CBD模型。

［关键词］高龄死亡率预测;动态模型;模型选择;模型稳健性

［基金项目］本文获中央高校建设世界一流大学(学科)和特色发展引导专项资金、教育部人文社会科学重点研究基地重大项目“基于大数据的精算统计模型与风险管理问题研究”(16JJD910001)资助。

［作者简介］王晓军,博士,中国人民大学统计学院院长，中国人民大学风险管理与精算中心主任,教授，博士生导师,研究方向:风险管理与精算;路  倩,中国人民大学统计学院博士研究生,研究方向:风险管理与精算学。

Comparison and Selection of Mortality Models for Senior Population

WANG Xiao-jun,LU Qian

Abstract：The mortality modeling of senior population is the basis for population forecasting,pension cost and debt assessment,and longevity risk management.In mainland China,age-specific mortality data of the elderly population is very limited and volatile.How to choose a suitable mortality model for China's senior age data has become an important research topic.This paper reviewed researches on mortality prediction models,and the senior population mortality data from Taiwan was adopted to fit the eight mortality models commonly used in the literature such as LC,CBD and Bayesian hierarchical model and compared the fitting and predictive effects and the robustness.Next,the paper modeled and projected the smoothed senior age mortality data in mainland China with CBD and Bayesian hierarchical model.The results showed the Bayesian hierarchical model could capture the historical fluctuations of the data and the prediction intervals covered the true value of mortality but had a broader interval and unreasonable survival curve.In comparison,the CBD model had better fitting and forecasting effects,with reasonable prediction intervals and survival curve.Therefore,for the longevity risk measurement,CBD mortality model was recommended.

Key words：senior age mortality forecasting;Stochastic model;model selection;robustness of the model