基于有限人口数据的死亡率预测与年金偿付能力评估

Mortality Projection and Solvency Assessment of Annuities with Limited Data

鉴于我国人口普查数据稀缺,抽样调查数据质量不高给人口死亡率预测带来的不利影响,本文在贝叶斯MCMC研究框架下利用贝叶斯因子和离差信息准则进行死亡率预测的模型选择和拟合效果的评估,并进一步比较了不同模型和数据组合下年金的定价、统计特征、风险度量和偿付能力资本要求。结果表明Lee Carter有限数据模型和三年高质量普查数据的组合能有效降低模型离差,提高死亡率预测的精度,并且能更好抓住年金价格分布的尖峰厚尾特征,结合TVaR风险度量能有效缓解Solvency II中基于VaR的方法缺陷,更准确地评估年金产品中的长寿风险。

In view of the adverse effects made by scarce Census data and inferior quality Population Sample Survey on mortality projection,this article aims to make a study on mortality model selection and model fitness using Bayesian factor and DIC(deviance information criterion).Further,the article compares annuities'price,statistic characteristics,risk measurement and solvency capital requirement among different model-data combinations.And the results show the Lee-Carter limited data model combined with the three years of Census data can effectively reduce model DIC and improve the projection precision,and these will help to seize the peak and fat tail characteristics of annuity price distribution.The combination along with TVaR risk measurement can amend the flaw of VaR method in Solvency II so as to measure longevity risk of annuity more accurately.