A family of fractional age assumptions

This paper introduces a unifying family of fractional age assumptions (FAAs ) whose members include the familiar uniform distribution of deaths, consta nt force, and Balducci assumptions. The family also includes a wide range o f alternative assumptions that can be used when those mentioned above are i nappropriate. FAAs combined with life table probabilities allow one to fully specify the age at death distribution. Traditionally, a single FAA is applied consisten tly across all ages. However, this frequently produces forces of mortality between integer ages that are inconsistent with the pattern of mortality ra tes across ages. In this paper, we introduce the idea that the FAA can be a llowed to vary across ages so as to produce a more reasonable force of mort ality function and more accurate actuarial present values. Our family of FAAs is also considered in estimating mortality rates. Rather than making an arbitrary assumption in order to express probabilities and densities in terms of the mortality rate, we allow the data to determine th e FAA. (C) 2000 Elsevier Science B.V. All rights reserved.