AI 中文总结
本文从精算视角对比可靠性理论与活力建模，二者可生成Gompertz等死亡率定律，结合加拿大数据研究相关因素，构建生物年龄定义，为死亡率与衰老研究提供精算洞见。
AI 中文摘要
本文从统一的精算视角出发，通过研究可靠性理论与活力建模，探讨人类死亡率的两种机理解释。尽管这两种方法源于不同的衰老机制，但我们证明在适当假设下，二者均可自然生成Gompertz定律，且可扩展以产生Makeham定律及晚年死亡率平台期。利用加拿大死亡率数据，我们考察了每种方法的经验表现，并强调了异质性、外在风险与随机随机性的作用。此外，我们在两种方法下分别构建了生物年龄的定义，分析了主观生存信念如何因参数误设而产生。我们对这两种方法的比较，为Gompertz死亡率的自然基础以及衰老、脆弱性与死亡的解释提供了精算洞见。
英文摘要
This paper studies two mechanistic explanations for human mortality by examining reliability theory and vitality modelling through a unified actuarial perspective. While the two approaches arise from different ageing mechanisms, we show that both can naturally generate the Gompertz law under suitable assumptions and can be extended to produce the Makeham law and late-life mortality plateaus. Using Canadian mortality data, we investigate the empirical behaviour of each approach and highlight the roles of heterogeneity, extrinsic risk, and stochastic randomness. Furthermore, we develop parallel definitions of biological age under both approaches and analyse how subjective survival beliefs emerge from misspecified parameters. Our comparison of these two approaches provides actuarial insights into the natural foundations of Gompertz mortality and the interpretation of ageing, frailty and death.
