多维分层人口随机死亡率模型及其应用  

Hierarchical Population Stochastic Mortality Model of Multi-Dimension and Its Application

作　　者：赵明 王晓军[2] ZHAO Ming;WANG Xiao-jun(School of Finance,Capital University of Economics and Business,Beijing 100070,China;School of Statistics,Renmin University of China,Beijing 100872,China)

机构地区：[1]首都经济贸易大学金融学院,北京100070 [2]中国人民大学统计学院,北京100872

出　　处：《数理统计与管理》2024年第6期973-984,共12页Journal of Applied Statistics and Management

基　　金：教育部人文社会科学研究青年项目(23C10038050);北京市属高等学校优秀青年人才培育计划项目(BPHR202203166);首都经济贸易大学青年学术创新团队项目(QNTD202104);国家社科基金后期资助项目(23FJYB024)。

摘　　要：人口随机死亡率预测是养老金管理者和保险公司度量长寿风险的基础,其中多人口随机死亡率建模是当前研究的前沿与热点。本文将传统的单一维度下性别人口或地区人口模型,扩展为性别人口与地区人口相联合的多维模型,提升人口随机死亡率建模的系统性。同时,引入超参数构建分层模型,采用马尔可夫链蒙特卡罗模拟和数据克隆技术改进参数估计方法,以弥补传统方法中先验假设主观性强和拟合结果不稳定的问题。通过比较研究,发现多维分层人口随机死亡率模型不仅提高了样本内拟合优度与短期预测效果,并且长期预测结果更加符合人的生物规律。Stochastic mortality forecasting is the basis for pension managers and insurance companies to measure longevity risk.Modeling multi-population stochastic is the forefront and hotspot of current research.This paper extends the traditional mortality model under a single dimension to a multi-dimensional model combining gender population and regional population,so as to improve the systematicness of the multi-population stochastic mortality model.At the same time,prior parameters are introduced to construct a multi-dimensional hierarchical mortality model,and data cloning technology and Markov Chain Monte Carlo simulation are used to improve the parameter estimation method,so as to make up for the problems of strong subjectivity of prior assumptions and unstable fitting results in traditional methods.Through comparative research,it is found that the multi-dimensional hierarchical stochastic mortality model improves the scientificity of mortality modeling and the rationality of prediction results.It not only obtains better in sample goodness of fit and short-term prediction effect,but also the long-term prediction results are more in line with human biological rules.

关 键 词：人口死亡率 贝叶斯分层模型 数据克隆 长寿风险 

分 类 号：F840.6[经济管理—保险] O212[理学—概率论与数理统计]