《保险研究》20230905-《仿射死亡率模型长期预测的优化与分析——考虑非完整近期队列数据》（李玉龙、Michael Sherris、Andres M.Villegas、Jonathan Ziveyi）

［摘   要］死亡率建模与预测是精算科学的重要基础，而仿射死亡率模型作为一种经典的连续时间随机模型被大量地应用于评估系统性死亡率的发展，其中模型构建的一种常用方法是卡尔曼滤波算法。本文针对传统卡尔曼滤波算法在建模过程中自动忽略近期非完整队列数据的情况，借鉴机器学习和贝叶斯算法中迭代学习的理念，对传统算法进行了拓展，从而将近期非完整队列数据应用于模型拟合与预测中。通过量化分析对比证明了基于拓展算法的模型在预测方面，尤其是长期预测中，有两方面的优势：更好地捕捉了系统性死亡率风险的变动，避免了对长期长寿风险的低估；在预测精度方面有了较大的提升，特别是在长期预测时优势更为明显。

［关键词］非完整数据应用；卡尔曼滤波算法；模型长期预测；养老产品定价

［基金项目］本文受Society of Actuaries Center of Actuarial Excellence Research Grant 2017-2020：Longevity Risk：Actuarial and Predictive Models，Retirement Product Innovation，and Risk Management Strategies 和CEPAR Australian Research Council Centre of Excellence in Po

［作者简介］李玉龙，博士，就职于中国精算师协会国际部；Michael Sherris，澳大利亚新南威尔士大学商学院风险精算系教授；Andres M.Villegas，澳大利亚新南威尔士大学商学院风险精算系讲师；Jonathan Ziveyi，澳大利亚新南威尔士大学商学院风险精算系副主任、副教授。

Improvement and Analysis of the Affine Age-Cohort Mortality Projection Considering Incomplete Cohort Data

LI Yu-long,Michael Sherris,Andres M.Villegas,Jonathan Ziveyi

Abstract：Mortality modelling and projection is important in the field of actuarial science,in which affine mortality models,as classic continuous-time stochastic models,are widely used,especially for assessing the systematic mortality improvement.The traditional Kalman Filter Algorithm (KFA) is a classical method used in the affine framework for model calibrations.In this paper,learning from the concepts of machine learning and the iterative learning of the Bayesian algorithm,we extend the traditional KFA by incorporating the recent incomplete cohort data into model calibration and projection processes.The quantitative comparison results show that,compared to the traditional KFA,the extended KFA have two advantages,especially for long-term projection.It can better capture the future systematic mortality movements,thus avoiding the underestimation of the longevity risks;it significantly improves the projection accuracy,especially for the long-term projection.

Key words：incomplete cohort data；Kalman Filter Algorithm；long-term mortality projections;pricing of pension products