二维非参数死亡率修匀模型的对比分析——基于2000-2020年中国人口死亡率数据

Comparative Analysis of the Non-parametric Bivariate Smoothing Model of Mortality Rates:Based on the Mortality Data of Chinese Population from 2000 to 2020

人口死亡率是评估寿险产品风险和确定保费定价策略的关键指标。基于2000—2020年中国分城乡、性别的人口粗死亡率数据,本文对比了传统的二维Whittaker修匀模型以及近些年得到广泛验证的二维离散Beta核修匀模型和二维泊松P-样条修匀模型的修匀效果。结果显示:二维Whittaker修匀结果的光滑度最好,另外两种模型的修匀结果光滑度在不同人口群体中存在差异。总体来看,二维离散Beta核修匀结果的拟合度最优。三种死亡率修匀模型均会低估边端年龄的死亡率,各模型的低估程度在不同人口群体中存在差异。在对人口死亡率进行修匀时,应根据研究的实际问题和人口特征选取对应的修匀模型,也可以考虑用组合模型的方式进行修匀。

The population mortality rate is a key indicator for evaluating the risk of life insurance products and determining premium pricing strategies.Based on the crude mortality rates data of male and female populations in urban and rural areas in China from 2000 to 2020,this study compares the smoothing effects of the traditional bivariate Whittaker graduation model with the widely validated bivariate discrete Beta kernel graduation model and the bivariate Poisson P-spline graduation model in recent years.The results indicate that the bivariate Whittaker graduation model exhibits the best smoothness.The smoothing effects of the other two models vary across different population groups.Overall,the bivariate discrete Beta kernel graduation model shows the best fit.All three mortality graduation models tend to underestimate mortality rates at the upper and lower age ranges,with varying degrees of underestimation across different population groups.When smoothing population mortality rates,the choice of the appropriate graduation model should be based on the specific research question and population characteristics.Alternatively,a combination of models can be considered for smoothing.