成分数据视角下的死亡率建模与长寿风险度量

Mortality Modeling and Longevity Risk Measurement from a Compositional Data Perspective

摘要: 该研究旨在通过引入成分数据分析(Compositional Data, CoDa)方法，对经典的Renshaw-Haberman (RH)死亡率模型进行改进，以更精确地度量和预测人口老龄化背景下的长寿风险。论文核心方法是利用中心对数比(Centered Log-Ratio, CLR)变换，将具有总和约束的死亡人数分布数据转化到无约束的欧氏空间中进行建模。通过对西班牙和澳大利亚男性死亡率数据的实证分析，研究表明，与传统的Lee-Carter (LC)模型和RH模型相比，基于成分数据框架的CoDa-RH模型在平均绝对误差(MAE)和艾奇逊距离(AD)等评估指标上表现更优。该模型不仅提高了预测精度，其预测结果还显示出与历史数据更好的拟合度，并呈现出更快的死亡率改善趋势，从而得出较高的预期寿命预测值。最终，论文将模型应用于终身生存年金精算现值的测算，结果显示新模型评估的长寿风险敞口更大，为养老金和保险行业提供了更可靠的量化管理工具。

Abstract: This research aims to refine the classical RH mortality model by incorporating a Compositional Data approach, enabling more precise measurement and forecasting of longevity risk against the backdrop of population aging. The methodological core involves applying CLR transformation to convert constrained mortality distribution data—characterized by a fixed-sum constraint—into an unconstrained Euclidean space for subsequent modeling. An empirical analysis of male mortality data from Spain and Australia demonstrates that the CoDa-RH model achieves superior performance relative to both the traditional LC and standard RH models, as measured by key evaluation metrics including MAE and Aitchison distance. The proposed model not only enhances predictive accuracy but also exhibits improved alignment with historical data and reflects a more pronounced trend of mortality improvement, leading to higher life expectancy forecasts. In its final application, the model is employed to estimate the actuarial present value of life annuities. The results indicate a larger longevity risk exposure under the CoDa-RH framework, offering pension and insurance sectors a more reliable quantitative tool for risk management.