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.

This paper considers equity, or fairness, as being based on with-profits life insurers acting in accordance with their contracts. It uses the principles of with-profits business in conjunction with a legal approach to derive implied terms in with-profits contracts. The author examines certain situations of conflict between with-profits policyholders and shareholders. The paper does not regard all concerns put forward on behalf of policyholders’ interests as justified in practice: actuaries and regulators have been alert to issues and in many cases have taken appropriate action. However, it does suggest a number of practices that may be unfair. The paper also suggests that the current process for the reattribution of an inherited estate may favour shareholder interests over policyholder interests.

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.

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.

The object of the following notes is to state somewhat more fully and formally a method (first published in the Insurance Record for 10 March 1905) of approximating to the reserves required for whole-life assurances, with due regard to the influence of selection; and to illustrate the practical application of the method.

In the course of a paper read before the Institute in January 1885 (J.I.A., xxv, 141), I suggested a certain method of making approximate valuations on different bases of the liabilities of a life assurance company under its whole-life policies. Shortly afterwards I had occasion to make a valuation of the liabilities of a particular company, and I took the opportunity of testing the suggested method of approximate valuation by actual comparison of the results arrived at by its application with those derived from a rigidly accurate class valuation, and I have thought that it would be interesting to the members of the Institute to have an explanation of the process employed in making use of the approximate method, and a statement of the results of the comparison.

The paper is an attempt to bring out the exact relationship between what has been called the ‘modified osculatory process’ and the older formulae of osculatory interpolation. The conditions upon which the modified process is stated to be based are shown to be insufficient in themselves to produce a determinate formula even after the degree has been made as low as possible, and a general formula is derived which satisfies these conditions and of which the formulae hitherto employed are particular cases. The general formula contains, as might be expected, certain arbitrary constants which reflect the relaxation of certain of the conditions insisted on by the older formulae.

Illustrative graduations are performed by means of the general formulIllustrative graduations are performed by means of the general formula

and the results are compared with previous graduations of the same data by Jenkins's fifth difference formula (which may be obtained by putting b=0 in the general formula), viz.:—

This is the particular case of the general formula which has hitherto been used in practice.

The influence that occupation has upon health is a subject that has hitherto attracted but little attention, for though in the works of one or two writers on vital statistics it has been slightly alluded to, no work has yet appeared which, while founded on direct observation, has been devoted to the treatment of this subject.