ABSTRACT

The law of uniform seniority is an actuarial principle which justifies the replacement of an annuity on joint lives of unequal ages by an annuity on a single life, often computed at a different rate. Gompertz's law of mortality is a prime example of distribution which meets this condition. This paper proposes an extension of this principle to the case of two dependent lives and relates it to aging concepts. In the important special case of a bilinear averaging function, it is shown that the lifetimes have a dependence structure which is Archimedean and marginal distributions from the same scale family. This leads to both functional and stochastic representations for these models, which enjoy closure properties with respect to some common operations. The dependence and aging properties of the models are then discussed. The challenges involved in a multivariate extension are also mentioned.

摘要

统一资历法是一项精算原则，它证明用单一生活的年金代替年龄不等的共同生活的年金是合理的，通常以不同的比率计算。Gompertz 的死亡定律是满足这一条件的分布的主要例子。本文建议将此原则扩展到两个依赖生命的情况，并将其与老龄化概念联系起来。在双线性平均函数的重要特殊情况下，表明生命周期具有依赖结构，即来自同一尺度族的阿基米德分布和边际分布。这导致了这些模型的函数和随机表示，它们在一些常见操作方面享有闭包特性。然后讨论模型的依赖性和老化特性。