It is commonplace to remark that probability lies at the root of actuarial science. It is equally commonplace that there has been—and still is—considerable dispute over the definition of probability and that such dispute is usually of little consequence in practical calculations. This being so, some may wonder why I have chosen to ventilate once again the philosophical problems which encompass the concept of probability and which commonly bedevil discussions of what is meant by propositions of the form ‘The probability of x is y’ or ‘A is more probable than B’. The solutions which may be offered to this type of problem are not likely to affect the amount of a surrender value or the contribution scale of a pension scheme. On occasion they may affect the answers to estimation problems or decisions based upon significance tests, although even here the differences between the results yielded by alternative methods of approach are commonly negligible.

1. Terms of Reference

Our terms of reference were as follows:

To prepare a study on the impact of pension payments on the national economy, with particular reference to the following matters:

The financial and economic effects of pension rights of all kinds (under National Insurance, Civil Service and Local Government schemes, schemes for nationalized industries and under private schemes, both by private funds and with Life Offices) having regard to the future population trends in the United Kingdom and, in particular, the growing number of aged persons in the population over the next few decades.

The relation between the trend of productivity and the growth of pension rights. The financial and economic effects of funding and assessmentism. The financial and economic effects of funding and assessmentism.

The two-fold purpose of this paper is:

(i) To hypothesize the existence of a Basic Curve of Deaths, a curve to which it is suggested all curves of deaths are, as it were, striving to attain—the ‘idea’ of a curve of deaths, almost in a Platonic sense, a curve applicable not only to humanity, but equally to all forms of life.

(ii) To seek a representation of that curve by a function containing as few parameters as possible, on the principle that while there are other functions which fit the observations more exactly, we here prefer a simple function which fits them well enough.

The general impression gained from a broad review of the earlier activities of the Institute is that the actuary of those days appears to have been less concerned with the question of the investment of funds than the actuary is to-day. There are several factors which lend support to this impression. First, in those earlier years the actuary, probably being preoccupied with the purely actuarial side of life assurance, friendly society and pension fund business, may have been content to leave the matter of investment to others and to accept their advice regarding the rates of interest to be assumed in his actuarial calculations. Secondly, both the field of investment and the volume of funds requiring investment being very much smaller, the problem may not have appeared to justify much greater attention than was paid to it. Perhaps the most likely reason, however, was that the practice of investment may have been regarded more as an art than a science and as a subject therefore which did not readily lend itself to an actuarial approach.

Medical and social progress over the past 50 years has resulted in a large increase in the expectation of life, and this, together with a declining birthrate, has caused an increase in the proportion of old persons in the population. In 1901 less than 5% of the population of England and Wales was aged 65 and over; by 1949 the estimated percentage had increased to 11% and must inevitably increase still further in the future. A result of this is that more and more attention is being given to diseases of old age and in fact a new specialized branch of medicine, geriatrics, seems to have arisen. Heart diseases form by far the largest group of causes of death in old age and in 1949 were the certified cause of death in 37% of the deaths in England and Wales at ages 65 and over (Table 1). Even in the age-group 55-59 heart disease was responsible for 24% of all deaths in 1949.