随机动态死亡率模型的统计性质及应用研究

随机动态死亡率模型的研究是长寿风险度量与管理的理论基础。长寿风险对个人养老、保险精算、社会保障乃至国家的安定团结都至关重要。本项目综合运用保险精算、统计推断、大数据分析、随机过程建模、金融投资等相关理论与方法，首先深入分析各种经典动态死亡率模型，讨论改进模型参数估计的统计方法，提出模型的适用性原则；其次，对我国人口数据进行大数据分析，探讨基于机器学习方法的死亡率模型，建立死亡率序列的数据模型；第三，构建我国高龄人口随机死亡率模型，研究人口预期寿命分布并讨论其波动性；最后，将以上理论结果应用于长寿风险的度量管理中，得出基于破产概率理论的长寿风险量化方法，构造相互保险养老年金精算模型，讨论年金池的风险量化与管理，给出年金池平稳运行的参数指标体系，创造性地解决系统长寿风险。本项目的完成不仅丰富死亡率模型和长寿风险的相关理论，也为社会保障部门提供相关的理论依据和技术支撑。

The study of stochastic dynamic mortality model is the theoretical basis of longevity risk measurement and management. Longevity risk is very important for personal pension, actuarial insurance, social security and even the stability and unity of the country. This project comprehensively uses actuarial theory, statistical inference, big data analysis, stochastic process modeling, financial investment and other related theories and methods. First, we deeply analyze various classic dynamic mortality models, discuss statistical methods to improve model parameter estimation, and propose the applicability principles of the model. Secondly, big data analysis is conducted on China's population data, a mortality model based on machine learning methods is explored, and a data model of mortality series is established. Third, construct a stochastic mortality model for the elderly population in China, study the distribution of life expectancy of the population and discuss its volatility. Finally, the above theoretical results are applied to the measurement and management of longevity risk, and the longevity risk quantification method based on the ruin probability theory is discussed, and the mutual insurance pension actuarial model is constructed. Discuss the risk quantification and management of the annuity pool, and give a parameter index system for the smooth operation of the annuity pool, so as to creatively solve the longevity risk of the system. The completion of this project not only enriches the relevant models of mortality models and longevity risks, but also provides relevant theoretical basis and technical support for the social security department.