The paper describes in some detail the statistical methods that may be used for analysing mortality data from medical and epidemiological studies, with particular reference to quantifying survival and the risk of mortality and to comparing the experience with a standard.

The complete expectation of life at birth ė0 is frequently used as a measure of the level of mortality of a population. It is also used for assessing trends in mortality and trends in mortality differentials. Although the relationship between mortality and expectation of life is essentially reciprocal, the exact connexion is rather more complicated, and becomes important when, for example, trends in differentials are analysed.

In this paper, the relationship between mortality and expectation of life is explored in some detail, and formulae are developed for analysing the effects of mortality changes on expectation of life, and trends in mortality differentials on ė0 differentials.

Unlike Keyfitz (1977), who concentrates on the proportional change in ė0 corresponding to equal proportional changes in mortality at all ages, we study the relationship between absolute changes in mortality, generally different at different ages, and the corresponding absolute change in ė0.

It is demonstrated that two populations may experience diminishing mortality differentials and at the same time widening ė0 differentials. Numerical examples are given using Australian data over the periods 1921–71 and 1971–79.

Although the formulae in the paper relate solely to the expectation of life at birth, the methods and formulae are readily adapted to expectations of life at other ages and indeed, temporary expectations.

1.1. This paper explores the possibility that a company which sells unit-linked policies with death and maturity benefit guarantees may follow an investment strategy which reduces the risks associated with them. It originated when the author was requested by the Institute to study papers on the subject by P. P. Boyle, M. J. Brennan and E. S. Schwartz of the University of British Columbia in Canada and also a paper presented to the Society of Actuaries in Ireland by J. C. Fagan.

In an earlier introductory paper (J.I.A.107, 513), Balzer and Benjamin (1980) presented a model of an insurance system with delayed profit/loss sharing feedback from insurer to insured. The system was considered from a general control and dynamic systems theory viewpoint. Certain fundamental concepts were introduced and the dynamic responses of cash flow f(k) and accumulated cash flow fa(k) to an isolated group of unpredicted claims presented. This paper takes the analysis further in a number of important ways.

The general structure and details of the mode1 of the insurance system can be found in the earlier paper.