基于模糊聚类的多人口死亡率模型研究

Multi-Population Mortality Model Based on Fuzzy Clustering

摘要: 面对严峻的全球养老局势，单独研究某个国家的死亡率效果往往欠佳，我们需要建立多人口死亡率模型来拟合和估计死亡率。研究多人口共同因子死亡率模型，可以更好地抓住被研究人口的共性和差异。由于大部分发达国家比我国的老龄化程度更深，本文由死亡率相互独立的Individual Lee-Carter模型提取14个国家和地区的年龄和时期效应，由三种聚类方法分别可视化。将共同年龄效应模型和联合K模型与模糊k-Means聚类和队列效应结合，构建四个新模型：模糊共同年龄效应模型、模糊联合K模型、r共同年龄效应模型和r联合K模型。数值结果表明与模糊k-Means聚类结合的模型，拟合和预测效果都很好。添加了队列效应的模型，受模型和出生年份限制，效果欠佳。所以共同因子死亡率模型可以提高预测精度和提供建设性建议。本文是利用机器学习研究多人口死亡率的有益尝试。

Abstract: In the face of severe global pension situation, the effect of individual study on mortality of a country is often not very well, we need to build multi-population mortality model to fit and estimate mortality. The study of multi-population common factor mortality model can better capture the commonness and difference of the studied populations. Most developed countries have a deeper degree of aging than China. In this paper, the Individual Lee-Carter model with independent mor-tality is used to extract the age and period effects of 14 countries and regions, three clustering methods are used to visualize them respectively. The common age effect model and Joint-k model were combined with fuzzy k-Means clustering and queue effect to construct four new models: fuzzy Common Age Effect model, fuzzy Joint-k model, r-Common Age Effect model and r Joint-k model. The numerical results show that the model combined with fuzzy k-Means clustering has better fitting and prediction effect. The model with cohort effect was not very effective due to the limitation of model and birth year. Therefore, the common factor mortality model can improve the prediction accuracy and provide constructive suggestions for countries and the insurance company. This paper is a useful attempt to study multi-population mortality using machine learning.