The original purpose of this paper—undertaken at request but not unwillingly—was to review the principles and practice of life-office valuations in the light of modern conditions. It was difficult, however, to deal satisfactorily with the principles of valuation in vacuo without reference to more fundamental principles. As a consequence the paper has become more ambitious in its scope than originally intended—and has threatened to run away with itself. The reader will perhaps be less disappointed if he is warned in advance that he is to be taken on a ramble through the actuarial countryside and that any interest lies in the journey rather than the destination.

The experiments described in this paper arose from some calculations made in connexion with the recent discussion on the mortality of life-office annuitants (J.I.A. lxxviii, 27) and are a natural development of the principles described in the paper submitted to the Centenary Assembly of the Institute (Proceedings, 11, 89). They fall into two groups. Those in the first, arising from an attempt to find an alternative method on which to base projections, have an affinity with those set out by Starke in his recent paper (J.I.A. lxxviii, 171), in that a formula for expressing mortality is derived essentially dependent on year of birth. There are, however, fundamental differences between the approaches, in that Starke is concerned mainly with an ad hoc expression for a derived function of qx without regard to the problem of computing functions, whereas the present experiments are concerned with (i) further developing actuarial technique based on the curve of deaths rather than on rates of mortality, and (ii) the calculation of actuarial functions without recourse to the usual methods of commutation columns. The second group of experiments is an extension of the gamma-function technique to the calculation of joint-life functions, including contingent assurances.

During the discussion on Beard's paper (J.I.A. lxxvii, 425) A. C. Edwards commented on the relatively heavy death-rate during the last twenty years among men in England and Wales who were aged 20–40 in 1916. He pointed out that, in the tables on the Trend of Mortality in England and Wales that appear in J.I.A. from time to time, there is a peak in the ratios of men's mortality to the 1930–32 standard that has moved from ages 45–49 in 1933 to 60–64 in 1944–48, and he put forward as a possible explanation that this age-group lost a number of its fittest members during the 1914–18 war and that the survivors who had been on active service have been suffering from delayed and cumulative after-effects. He added that the excess mortality at the top of the hump might be 10–15% and suggested that some marked changes in male annuitants' mortality in the 60's and 70's might be observed during the next few years.