《保险研究》20250504-《基于动态Nelson-Siegel模型的中高龄人口死亡率拟合与预测》（孙佳美、李雨欣）

［摘   要］中、高龄人口死亡率预测是人口规模预测的重要部分，也是人寿保险精算的重要数据基础。本文首先分析了中国大陆、中国台湾地区及HMD数据库中6个国家的中高龄人口死亡模式，发现死亡率随年龄的增长是非线性增加的；在此基础上，基于动态Nelson-Siegel模型对CBD模型的年龄效应进行了非线性改进，提出从时间和年龄两个维度对中、高龄人口死亡率进行动态拟合、预测和外推的模型；最后，分别利用CBD模型和本文提出的模型，基于HMD数据库中18个国家与中国台湾、中国大陆地区的分年龄、性别的人口死亡数据进行死亡率拟合与预测。结果表明，与CBD模型相比，本文提出的模型对历史数据具有更好的拟合度，并且具有更好的样本外预测性能：相对长期预测该模型的短期预测效果更好。此外，该模型对于高高龄人口死亡率的外推效果也相对更好。本研究试图为我国中高龄人口死亡率的拟合和预测提供参考。

［关键词］中高龄人口；死亡率；Gompertz模型；动态Nelson-Siegel模型；CBD模型

［基金项目］南开大学2023年本科教育教学改革立项（NKJG2023079）；南开大学2024年教学成果改革项目（NKJG2024197）。

［作者简介］孙佳美，南开大学金融学院副教授，硕士生导师，研究方向：统计与保险精算；李雨欣，南开大学金融学院精算学硕士研究生。

Fitting and Prediction of Mortality in Middle-aged and Elderly Population Based on Dynamic Nelson-Siegel Model

SUN Jia-mei，LI Yu-xin

Abstract：The mortality prediction of middle-and elderly population is an important part of population size prediction，and also an important data basis for life insurance actuarial science.This paper first analyzes the death patterns of the middle-aged and elderly population in mainland China，Taiwan China and six countries in the HMD database.It is found that the mortality rate increases nonlinearly with age.On this basis，and based on the dynamic Nelson Siegel model，the age effect of CBD model is improved nonlinearly，and a dynamic fitting，prediction and extrapolation model for the mortality rate of middle-aged and elderly population is proposed from the two dimensions of time and age.Finally，by using the CBD model and the model proposed in this paper，the mortality fitting and prediction are carried out based on the age and gender specific mortality data of 18 countries in HMD database，Taiwan China and Mainland China.The results show that，compared with the CBD model，the model proposed in this paper is more superior in fitting for historical data，and has better out-of-sample prediction performance and short-term prediction effect.In addition，the extrapolation effect of the proposed model for the mortality rate of the old-oldest age population is also relatively better.The conclusion of this study can provide reference for the fitting and prediction of the mortality rate of the middle-aged and elderly population in China.

Key words：middle-aged and elderly population;mortality rate;Gompertz model;Dynamic Nelson-Siegel model;CBD model