A law of uniform seniority for dependent lives

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.

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