学术 | 高光远研究员就Lee-Carter模型的年龄一致性实现方法在《Scand. Actuar. J.》发表论文
2021-05-01
我中心研究员高光远在《Scandinavian Actuarial Journal》发表论文。文章针对Lee-Carter模型在长期死亡率预测中存在的年龄不一致问题，提出了改进方法。论文使用inversed Epanechnikov kernel拟合Lee-Carter模型中各年龄的相对死亡率在年龄维度随时间的变化趋势。在时间维度上，本文使用和比较了几何和双曲下降函数对该趋势的拟合及样本外预测的方法。实证部分，样本涵盖1950至2016年15个国家的年度死亡率数据。结果表明，本文提出的改进方法在单一总体和多总体的模型框架下，实现的死亡率预测结果普遍优于Lee-Carter及其广泛应用的衍生模型。
论文题目
Age-coherent extensions of the Lee-Carter model
作者介绍
高光远，中国人民大学统计学院副教授、应用统计科学研究中心研究员。主要研究领域包括非寿险准备金评估方法，贝叶斯统计和MCMC，车险定价模型，车联网大数据分析，copulas，死亡率预测模型等。在精算、机器学习顶尖期刊发表多篇论文，如《ASTIN Bulletin：the Journal of International Actuarial Association》，《Insurance：Mathematics and Economics》、《Machine Learning》等；由Springer出版独著《Bayesian claims reserving methods in non-life insurance with Stan》；参与编著多本教材；主持慕课《非寿险精算学》建设；主持国家自科青年项目，Society of Actuaries科研项目等；参与国家社科重大项目等。
英文摘要
Age coherence describes the property that forecast mortality rates across ages will not diverge in the long run. Although intuitively and biologically reasonable, this property is lost when the seminal Lee–Carter (LC) model and almost all its existing extensions are employed. In this paper, we propose two effective extensions of the LC model, allowing for the geometric (LC-G) and hyperbolic (LC-H) decayed relative speed of mortality decline at each age, over the out-of-sample forecasting steps. Those approaches are based on the original in-sample estimates of LC, which are easy to obtain. An inversed Epanechnikov kernel is employed to model the geometric and hyperbolic parameters across ages, and unknown parameters are selected via a data-driven method. With little added computational cost to LC, our approaches incorporate the dynamic and rotating relative speeds of mortality decline over ages, recognize the growing difficulty of such declines at older ages, provide age-coherent forecasts of mortality rates in the long run, and is easily extensible to multi-population cases. Using a large sample of 15 countries, we demonstrate that LC-G and LC-H, as well as their multi-population counterparties, consistently improve the forecasting accuracy of the competing LC model and its single- and multi-population extensions.
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