Can the National Pension Scheme as a whole now be expected to maintain solvency? On what lines may the Scheme be expected to develop in the future? Should contracting out not have been permitted?

The temptation to go into these and other fascinating questions will be resisted as far as possible; it is proposed instead to confine the subject matter of this paper reasonably closely within the area implied in the title. In order to establish the context in which the present situation has arisen, it is appropriate, however, to begin with a very brief survey of the more recent history of national and private pensions in Britain before the passing of the National Insurance Act 1959, which will be referred to henceforward simply as ‘the Act’; the situation before the Act comes into operation will similarly be referred to as ‘pre-Act’. When the Act comes into operation two new situations will arise; ‘Contracted-in’ and ‘Contracted-out’. There are thus three conditions to consider, and as far as possible when using expressions in connexion with contracting out such as saving, extra cost, etc., it will be stated whether these are by comparison with the contracted-in or pre-Act position, lack of clarity on this point having been a source of confusion in some of the literature on the subject.

Dynamic programming, a mathematical field that has grown up in the past few years, is recognized in the U.S.A. as an important new research tool. However, in other countries, little interest has as yet been taken in the subject, nor has much research been performed. The objective of this paper is to give an expository introduction to the field, and give an indication of the variety of actual and possible areas of application, including actuarial theory.

In the last decade a large amount of research has been performed by a small body of mathematicians, most of them members of the staff of the RAND Corporation, in the field of multi-stage decision processes, and during this time the theory and practice of the art have experienced great advances. The leading force in these advances has been Richard Bellman, whose contributions to the subject, which he has entitled Dynamic Programming [1], have had effects not only in immediate fields of application but also in general mathematical theory; for example, the calculus of variations (see chapter IX of [1]), and linear programming (chapter VI).

An essential part of the work carried out by the actuarial profession is the valuation of reversionary interests or life interests for the purpose of calculating either estate duty or stamp duty. The number of actuaries who are engaged in this work regularly is very small, but most actuaries are probably asked to undertake such valuations at some time or other. The object of this paper is to discuss some of the principles upon which these valuations are based and to illustrate the application of these principles by means of examples drawn from the authors' own experiences.

Under the Finance Act 1894, Estate Duty is payable on the principal value of a property. This is defined in Section 7 (5) of the same Act as follows:

‘The principal value of any property shall be estimated to be the price which, in the opinion of the Commissioners, such property would fetch if sold in the open market at the time of the death of the deceased.’

The most difficult problem which faces the young actuary is undoubtedly that of explaining to his non-actuarial friends and relatives exactly how he earns his living. This problem is one small part of the more general problem of communication between the actuarial profession and the outside world. A further specific aspect of the problem arises, for example, when a valuation has been completed and its results have to be expressed in the form of a report to be read by a group of non-technical people.

The purpose of this paper is to discuss some of the principles which should be followed when writing such a report. There is more than one such possible set of principles and other actuaries may have rather different views on the preparation and presentation of reports. The basic approach which gives rise to the principles is, however, fundamental to report writing and this is the need for communication between the actuary and his client.

1. During the early 1950's the annual numbers of births in England and Wales varied little from an average of 675,000, but since then there has been a marked rise and in 1960 no fewer than 783,000 births were registered. This steep increase was unforeseen in official population projections, including the range of projections published by the Royal Commission on Population, and is likely to have serious repercussions in some quarters. For example, it will in due course result in an increase in the numbers of children of school age to well above the numbers on which plans for school building and teacher training were based.

2. In a paper presented to the Society a year ago (J.S.S.16, 85) the authors showed that the increase in births was attributable in part to an increase in marriage rates and in part to an increase in fertility rates, but the latest data available were those relating to 1957 when there were 723,000 births. No explanation could be offered for the further increase and, in deciding upon the number of births to be assumed in the early years of the projection contained in the paper, it was assumed arbitrarily that the numbers would decline from 750,000 in 1959 to 710,000 in 1963, the latter being the number calculated on the marriage and fertility bases thought suitable for the long-term projection.