This quotation is from the first of that long series of letters addressed to the Registrar General on the Causes of Death in England. Dr Farr was in 1839 appointed ‘Compiler of Abstracts’ in the newly created General Register Office. The saving of 30,000 deaths a year represented about 10% of the current number of deaths. It took some forty years to make that reduction in the death rate, which coincided with Dr Farr's career with the General Register Office.

In the twenty-year period 1936–38 to 1956–58 the Standardized Mortality Ratio for England and Wales fell by 21 % for males and 31 % for females. Measured from a much lower rate of mortality, the rate of improvement has been from four to six times greater than in Farr's day. What of the future?

It is now some ten years since it was accepted, cautiously at first, that computers might be of some value in performing ordinary clerical procedures. Since that time, they have been gradually installed at an everincreasing rate in offices of all kinds, including insurance offices. Our own Institute was, I believe, the first body to publish tables—the a(55) tables—which had been prepared by means of a computer, In some respects it is a pity that the insurance world in this country has not been more to the fore in utilizing this new equipment although, from the number of insurance people who attend any meeting connected with computers, it is not due to any lack of interest in new methods but rather to a cautious attitude concerning making use of equipment until it has been fully proved by actual field service. This is in contrast to the position in U.S.A. where the insurance offices have been well to the front in development of office use of computers; indeed, an insurance office there was the first non-governmental business user and that office now has four very large machines in full-time use. As a result of this we were fortunate to have had the very instructive surveys published by our sister body, the Society of Actuaries.

This paper is mainly concerned with the division of a trust fund between the beneficiaries, when an actuary is asked for a solution which, in his opinion, is fair to all parties concerned. It may be that the beneficiaries are all sui juris and form a closed class, in which case they approach the actuary as umpire, and adopt a passive role, at least until they have considered the implications of his recommendations. Alternatively, the actuary's report may be required to assist the Court to approve a scheme involving beneficiaries, e.g. infants, whom it is the Court's object to protect. In that case the actuary's role—as discussed later in the paper—is rather different, but it may still be necessary for him to state what in his judgment would be an impartial solution.

I. Equity-linked contracts have been the subject of discussions at the Faculty of Actuaries (J. B. Maclean, T.F.A.23, 327), the Institute of Actuaries Students' Society (R. H. Blunt and L. H. Lane, J.S.S.14, 259) and the Institute of Actuaries (J.I.A.84, 37). The papers delivered and the discussions devoted considerable space to the question of the desirability, from the point of view of both the industry and the public, of the issue of such contracts.

Since these discussions, several offices have entered the market both for assurances and for ‘self-employed’ annuity contracts, and this paper, recognizing the de facto position, is concerned with practical points arising from the issue of the contracts.

The last paper presented to the Institute on the general subject of investments was that by J. G. Day (J.I.A. 85, 123) in October 1958. He summarized and commented upon the actuarial approach as disclosed in the major post-war papers and the subsequent discussions on this subject and set forth succinctly the position that had been reached, so that there is no necessity for doing so again. However, a major development in the investment policies of life offices since then has been the increased interest in overseas investment, and it is the purpose of this paper to set forth some of the considerations affecting investment in this field.

In a series of trials with constant probability p of ‘success’ (S) and q ( = I–p) of ‘failure’ (F), the problems arise of determining the expected number of trials required to obtain a specified pattern of results (e.g. SSFSFFSSSFF), and of calculating the probability that such a pattern will appear in a given number of trials. We are here concerned essentially with ‘general’ patterns which may exhibit no clear regularity; many methods are available, and well known, for dealing with regular patterns (e.g. SSSSSS or SFSFSF), which do not apply to irregular ones. Feller, has shown how to solve the problems for general patterns, using an ingenious definition of the event corresponding to the appearance of the pattern whereby it becomes a recurrent event; his powerful general theory of recurrent events then applies and yields the required information by means of generating functions. A different method is given on page 171 of Bizley for finding the expected number of trials required to obtain a general pattern; this uses only the simplest mathematical tools but involves rather a lot of work for long patterns. Under each of these methods, however, every given pattern has to be treated individually and a separate calculation performed.