The application of sampling technique to statistical data, which a few decades ago was a rarity, has now become common practice. Our past President, Mr F. A. A. Menzler, in his presidential address said:

Sampling, in all its manifestations, has become almost a social and industrial routine. In this paper, by examining in some detail the application of sampling to a particular branch of actuarial work, namely pension fund valuations, an attempt is made to investigate the possibilities of its use in the actuarial-field. By the choice of pension fund valuations, which are a particularly complicated example of the actuarial technique, the investigation will, it is hoped, give a good insight into the sort of problems involved.

Is there a mathematical formula which will express the way in which mortality changes age by age? Many students have sought that will-o'-the-wisp but have had to confess failure. For example, Sir William Elderton says:

The object of this paper is to continue the discussion on the valuation and bonus problems of a life office that was recommenced in the recent papers by A. T. Haynes and R. J. Kirton (T.F.A. xxi, 141) and by F. M. Redington (J.I.A. lxxviii, 286). Both of these papers were concerned, inter alia, with the principle of matching assets to liabilities or, in Redington's graphic phrase, of immunizing the life fund against the effects of a change in the general level of interest rates. Immunization of a life fund containing with-profits policies was shown by Redington to have far-reaching implications, and it was clear from the discussion on his paper that different opinions were held about the exact character of the immunization that might be most appropriate. For a non-profits fund total immunization may or may not be a suitable ideal with which to compare the practical position, and this would depend, in particular, upon the relative size of the capital and other free resources available and upon the level of the surrender and paid-up-policy options granted. But it is the purpose of this paper to argue that, for a with-profits fund, far from being a suitable ideal to be either aimed at or departed from, total immunization (including absolute matching) represents a dividing line between a zone of rational departure from another and more natural ideal and a zone in which a change in the level of interest rates would produce indefensible results.

It is not usual in mortality investigations of insurance data to associate exactly one unit with each life. It is easier to use policies or sums assured or some variation of policies and sums assured. But a proper statistical test of graduated rates of mortality derived from such an investigation cannot be made unless the effect of the variable number of units associated with each life is known. Beard and Perks (1949, J.I.A. lxxv, 75) gave, for four different sampling processes, formulae for the variance of the distribution of deaths for a mortality study based on policies, and Daw (1951, J.I.A. lxxvii, 261) illustrated the formulae by numerical examples on various hypotheses. In particular, he showed that the sampling process employed had little effect on the numerical results, but that the frequency distribution of the number of policies held was very important. The formulae derived by Beard and Perks assumed that the frequency distribution of the universe of number of policies held was known.

Since the formation of the Demographic Study Group by the Students' Society at the end of 1949, much attention has been devoted by a small but keenly interested body of members of the Institute to the analysis of fertility and reproductivity. One of the aims of their researches has been to arrive at an independent method of assessing the degree of sufficiency of the numbers of births in this country for the replacement of the population. The present paper, founded as it is upon the ideas expressed at the Group meetings, is in essence a joint production with members of the Group, and their share in it is gratefully acknowledged.

In a paper read before the Institute in January 1936, E. W. Phillips discussed developments in computing machines and made the following prediction :