This paper provides a flexible way to address some ongoing challenges in mortality modeling, with a special focus on the mortality curvature and possible mortality plateau for extremely old ages. In particular, we extend the Gompertz law (Gompertz, 1825) by proposing a multi-factor exponential model, a framework that is able to capture flexible mortality patterns, and allows for a convenient estimation and prediction algorithm. An extensive empirical analysis is conducted using the proposed framework with a merged mortality database containing a large number of countries and regions with credible old-age mortality data. We find that the proposed exponential model leads to superior goodness-of-fit to historical data, and better out-of-sample forecasting performance. Moreover, the exponential model predicts more balanced mortality improvements across ages, and thus leads to higher projected remaining life expectancy for the old ages than existing Gompertz-based mortality models. Finally, the modeling capacity of the proposed exponential model is further demonstrated by a multi-population extension, and an illustrative example of estimation and forecast is provided.

本文提供了一种灵活的方法来解决死亡率建模方面的一些挑战，并特别关注极端年龄的死亡率曲率和可能的死亡率平稳期。特别地，我们通过提出一个多因素指数模型来扩展Gompertz定律（Gompertz，1825），该模型能够捕获灵活的死亡率模式，并提供方便的估计和预测算法。使用提议的框架和合并的死亡率数据库进行了广泛的经验分析，该数据库包含大量具有可靠的老年死亡率数据的国家和地区。我们发现，所提出的指数模型导致对历史数据的优越拟合优度，以及更好的样本外预测性能。而且，与现有的基于Gompertz的死亡率模型相比，该指数模型预测了各个年龄段的死亡率改善之间更加平衡的平衡，因此导致较高的预计剩余寿命。最后，通过多人口扩展进一步证明了所提出的指数模型的建模能力，并提供了估计和预测的说明性示例。