Written concurrently with the first item in C.M.I.R.3, the Faculty of Actuaries Mortality Research Group's paper determines a range within which mortality rates of Life Office Pensioners may be expected to change in the foreseeable future. Comparisons are made between the observed changes in pensioner mortality rates and those observed for the population of England and Wales, and reference is also made to the trends of mortality rates assumed in recent British population projections. From these considerations two forecasts are made, based upon “optimistic” and “pessimistic” future mortality assumptions, between which it is expected the actual future rates of mortality change will lie.

In the second part of the paper the financial effects of the range of forecasts are set out, when used to project the graduated pensioner Mortality Experience 1967-70 (C.M.I.R., 2, 57). The implications are illustrated in the context of two model funds, one based upon life offices' data, and the other based upon a non-insured pension scheme for which the contribution rates vary in accordance with the levels of future expected pensioner mortality.

The Paper discusses the general problem of appreciation and depreciation, with special reference to the relation between maturing assets and maturing liabilities, and describes a method of calculating the bonus-earning power of different classes of policy. This method is used to test the effect on bonus-earning power of two types of changes in interest rates:–

1. (a) a change, such as that caused by the War Loan conversion of 1932, which takes effect gradually; and

2. (b) a subsequent change, due to a rise in the rate of income tax, which has an immediate effect on the income from existing as well as investments.

Mr. President and gentlemen, I should like to express my pleasure at being back in the Faculty Hall, where I was privileged to listen to your interesting discussion last year on “The Growth of Pension Rights”. I am glad to find that the number of occasions on which economists and actuaries are not only on speaking terms but able to take counsel of one another is increasing, for I am sure that there are many problems, of which the future of pensions is only one, that can only be satisfactorily resolved through our joint efforts and deliberations. This conviction rests partly on my experience as a member of the Phillips Committee, which was heavily dependent both on the actuaries who served on it and on the members of the profession who, in one way or another, helped it along; but it is a conviction that is just as forcibly brought home to me when I look across the Atlantic to the inquiry that has been in progress since 1950 into the long-term trends in savings and investment in the United States—an inquiry carried out by economists but sponsored and largely financed by the Life Assurance Association of America.

In submitting a revised edition of the paper which I read before the Actuarial Society of Edinburgh more than six years ago, I wish to express the pleasure I feel that this, my first effort, should not only have proved of benefit to students, but that the Faculty of Actuaries consider it worthy of a place in their Transactions. The subject was taken up originally to condense the best actuarial opinions and bring together some of those practical questions which had been dealt with by actuaries of ripe experience. Premiums can be profitably discussed at almost any time, because an exchange of views is sure to shed light on some obscure point of more or less importance. The present time is peculiarly opportune for further discussion, because of the recent publication of the New Mortality Experience, and the knowledge of such statistics which we have all been gradually absorbing.

In the course of some recent work (cf. reference 2) it proved necessary to construct a life table from a set of graduated values of mx, the central death rate at exact age x. This meant that values of qx had to be derived in order to produce the life table from a given radix. Since the values of mx were known only for integer values of x, it was necessary to use an approximate method to derive the corresponding values of qx at each age. In this note we discuss briefly the approximations which we adopted. Our results are necessarily of an elementary nature and the principal reason for setting them down is to provide a reference for possible future use. It is perhaps worth pointing out that in a situation where the values of mx are given by an explicit mathematical formula values of qx may be obtained exactly using the results of reference 1.

In the Introduction to his famous Théorie Analytique des Probabilités, Laplace, after an eloquent summary of the progress of Astronomy from the days when every rare celestial phenomenon was regarded as a portent of human misery, to the verification in April 1759 of the perihelion passage of Halley's Comet, proceeds to say :—

“The regularity which Astronomy shows us in the movement of Comets exists, beyond doubt, in every phenomenon of nature. The curve described by a simple molecule of air or of vapour is regulated in a manner as certain as the planetary orbits: there is no difference between the two cases save our ignorance.

It has been remarked on many occasions that whilst there is a plethora of material which has been contributed to the Institute and the Students' Society on the actuarial valuation of liabilities, the subject of valuation of assets seems to have been consistently overlooked by all save one or two authors. We believe that a compelling reason for this apparent indifference to the subject may be found in the trend of interest rates within the experience of the actuaries who introduced the valuation techniques which a student may now tend to take for granted.

Consider Table 1, compiled from information given in a paper by C. M. Douglas, F.F.A., on ‘The Statistical Groundwork of Investment Policy’. During the period 1833–1912 the average annual rate neither exceeded £3. 11s. od.% nor fell below £2. 9s od.%, and in general the yield drifted slowly downwards.

The Address is a journey in three parts. The first part describes the world scene in the last century when the Institute was founded and traces the development of actuarial work to the present day. The current U.K. pension scene is then broadly reviewed and the journey ends with vistas of the future. The concentration of actuarial work towards life assurance and pensions is attributed to meeting the needs of the past and encouragement is given to the urgent extension of the work of the profession into wider fields.

The U.K. pension scene is described as being complex, confused and filled with uncertainty. The profession is urged to assist government actively and positively, to examine the expected future growth of pension funds, and to compare the financing of retirement benefits in the U.K. with other methods adopted in Europe.

Work in wider fields is envisaged as embracing general insurance, the health and care of the aged, banking and finance, and the appraisal of capital projects.

From the fact that a very large amount of capital has been of recent years invested in loans to foreign governments, the question of sinking funds and other kindred matters has come prominently into notice; and matters which at one time were only looked upon as belonging to the theory of compound interest, are now become of great moment to thousands of persons who have invested, or purpose to invest, their money in the above-mentioned class of security. Various causes appear to have led to the large increase in the popularity of foreign loans among certain classes of investors. No doubt, the rapid growth of unemployed capital has considerably reduced the rate of interest realizable on first-class home securities, and has induced persons anxious to obtain a high rate of interest to invest their money elsewhere. From the nature of the case, however, even a fairly high rate of interest would not generally be sufficient inducement for an investor to lend money to a perfectly irresponsible foreign government, which might at any time, if it thought fit, renounce all its past financial obligations. Whether the general practice of providing for the repayment of loans has arisen from the scruples of foreign governments to accumulate a large national debt like our own, or whether, on the other hand, it has been found necessary to give an undertaking to repay the loan over a term of years, in order to make the loan at all palatable to investors, I cannot say; but the fact none the less remains, that very generally provision appears to be made, in the case of loans by foreign governments, for repayment in a shorter or longer period of time.

All business is, to a greater or lesser extent, concerned with the taking of risk. This paper attempts to explain some of the main approaches that have been adopted in pursuing the concept of risk from a probabilistic viewpoint. The word ‘risk’ itself has been used fairly indiscriminately by writers, and thus gets given a number of different senses, but it has attained a clear and precise definition at various times and in different types of literature. Indeed we can distinguish three main avenues of development. The first is the pure economic concept, the second the actuarial approach, and the third the more recent linkage of risk analysis with the general approach to decision-making under uncertainty.

In this paper, everyday actuarial data have been examined by means of standard statistical techniques. The data in question have been drawn from the publications of the Continuous Mortality Investigation Committee, and the methods of statistical analysis have been applied to investigate the nature and extent of the heterogeneity which may exist in those data.

This is the preamble to the petition presented to the Secretary of State's office of the British Parliament in April 1757 by the promoters of ‘The Corporation for Equitable Assurances on Lives’, the seed from which modern life insurance has sprung. It is undoubtedly the clearest statement made as to the purpose and justification of the life insurance industry and stands as a challenge to those engaged in it.