The considerable public discussion of the past two years on the subject of our social insurance schemes and their post-war reconstruction has culminated in the publication of the Government's plans as a White Paper (Cmd. 6550–1). At present, social insurance in this country (now to be called National Insurance) is divided into a number of independent sections, each with its own statistical arrangements covering a large part of the population. At the same time some aspects of the whole population are regularly surveyed by the Registrars-General by means of an independent system of recording. The Government's plan greatly expands the field of insurance to cover all classes and groups. Before this unified plan can begin to function, fresh statistical machinery will have to be prepared, adequate to the task of keeping it efficiently in operation, and there will in consequence be a great opportunity for coordinating, simplifying and generally improving the national population records as a whole.

The origin of savings connected with human life was not a particularly happy one in France. A certain Neapolitan named Lorenzo Tonti submitted to Mazarin, the Finance Minister of ‘Sun King’ Louis XIV, a savings plan, the profits from which would help to replenish the sadly depleted royal coffers of this grandiose monarch. The plan was called a ‘Tontine’ after its originator and provided for a lump sum to be divided amongst the survivors of those who had contributed after a period of say 10 to 15 years. The ‘sales psychology’ was good as the individual is normally of the opinion that he will outlive his contemporaries. Unfortunately the results were disastrous as Parliament refused to ratify the royal edict of 1653 and Mr Tonti was clapped in the Bastille.

The name of Lewis P. Orr is an honoured one in the history of medico-actuarial literature. It may well be claimed that his paper on “The selection of lives”(T.F.A. 8, page 103) and the revised edition (T.F.A. 13, page 181) were for many years the standard British works on the medical aspects of life assurance underwriting. His earlier paper (T.F.A. 6, page 55) on “Research in life assurance”—submitted to the Faculty in 1911—may, in its consequences, have been even more important because it set the actuaries of the time thinking, and from that, years later, arose the Continuous Mortality Investigation of the Institute and Faculty of Actuaries; but it is with the subject of the two later papers that we are now concerned.

In the early days of actuarial science investments were selected with the emphasis on capital security, with maximum interest as a secondary consideration. In such conditions pure interest represented almost the whole of the investment return and it was natural that interest should be regarded as a stable element in actuarial calculations, while risk arose almost entirely under the mortality heading.

Consider a continuous probability distribution of a variable x measured from its mean in units of its standard deviation, and suppose that deviations from the mean are taken irrespective of sign; let px represent the ordinate applicable to x (this ordinate is, of course, the sum of the original ordinates at + x and — x). We then have

, and we write .

In venturing to bring this subject before the Institute to-night, I am conscious of inviting attention to a matter which has been frequently treated before and by far abler hands than mine. I at once confess that I have little original matter to bring forward; indeed, the main object of this paper is to endeavour to bring into one focus and to a common standard of criticism the various formulas for ascertaining the rate of mortality, which have already been so often discussed in this room. The expression “rate of mortality” is advisedly used here instead of “exposed to risk”, because it would seem that attention has hitherto been unduly centred in the latter.

An allusion made by Mr. Jellicoe to this subject, in a paper read before the Institute of Actuaries on the 28th November, has induced me to place on record the conclusions at which I had arrived after a somewhat recent consideration of the question.

It appears to me that the buyer of a policy by way of investment, in considering the price at which he should purchase, should come to his decision entirely independent of what might be the Office value. The two values have no connexion whatever one with another. In the one case the purchaser is about to make an investment; in the other, the Office proposes to redeem a liability.

One of the most striking features in the history of Life Assurance business during the past few years is the marked increase—both absolute and proportional—which has been shown in the number and amount of policies effected under the Endowment Assurance plan. There is every reason to expect that this increase will continue, and that ere long Endowment Assurances will divide honours with whole life policies as regards importance in the periodical valuations. It is consequently very desirable so to improve the methods of valuing such policies as to minimize the amount of labour involved, and it will become more and more necessary to abandon methods which answered very well so long as Endowment Assurances were looked upon as “Special Policies”, but which are extremely cumbersome when applied to a large mass of contracts. The shorter methods that have hitherto been suggested, though admirably adapted for use in test or check valuations, involve an error which many actuaries will consider too appreciable to be neglected, more especially as the approximate methods nearly always bring out a reserve which is smaller than the true reserve, and it accordingly becomes desirable to seek some process that will be free from this objection.

The remainder form of Newton's formula of interpolation with divided differences has been known for at least 37 years; yet actuaries have taken hardly any notice of the complete formula which ought to be one of their principal tools. It will, therefore, not be superfluous to begin by reproducing the very elementary proof from first principles.

A Report with the above title, which forms Section B of this paper, was presented at the conference at Hythe, Kent in September 1977 of the General Insurance Study Group, which is sponsored jointly by the Institute and the Faculty. The conference was attended by about sixty people, nearly all non-life practitioners and nearly all actuaries.

Previous papers on technical reserves had discussed various statistical methods of estimating outstanding claim reserves, and in some cases had included some data to provide numerical examples of the use of the methods. In our report we chose to start with some data and to look at the degree of stability in those data. Inspection of the data showed remarkably stable patterns and it was apparent that a simple method not previously described based on average payments was likely to be satisfactory for estimating the reserve for outstanding claims. The report then seeks to explain why the authors consider that this method has advantages over two well-known but more complicated methods.

The paper describes the main features of the market in traded endowment policies (TEPs) and the role of the main players in the market. The controversial, and related, issues of how to put a value on a traded endowment policy and the information given to investors are examined. The issues facing life offices whose policies are traded are discussed.

It has been represented to me that, in view of the influential position occupied by M. Violeine, the quasi official and authoritative character of his book, and the currency likely to be thereby imparted to the erroneous principles employed by him in the treatment of problems of the class to which the first of those I have discussed belongs;—I say it has been represented to me that in these circumstances it might be well to be a little more explicit as to his manner of proceeding. In my discussion of the problem in question I did enough, I believe, to shew that M. Violeine's solution is certainly erroneous. I admit however that I did not succeed to my own satisfaction (nor apparently to that of others) in precisely hitting the blot in it, and, as it were, reducing it to its elements. I think that from the consideration I have since given to the matter, I am now able to point out the fallacy by which it is vitiated, and I therefore willingly accede to the suggestion that has been made to me.

The ordinary member of a pension fund, if asked whether there is any connection between the high cost of living at present oppressing him and the security of the pension to which he looks forward to support him in his old age many years hence, would probably fail to discover that the one is related to the other. The financial position of pension funds is, however, fundamentally affected by the sudden drop in the purchasing power of the sovereign during the last few years and more directly by the enhanced scales of salaries or wages which have resulted from the change in the value of money, and it is to be feared that in many funds a very serious position has to be faced. The actuary who is called upon to advise as to the situation and to formulate remedies by which equilibrium may be restored has not only difficult professional problems to grapple with, but, having made up his mind as to the course to be recommended, he has to carry with him the responsible officers of the fund, who in their turn have to secure the co-operation of the employer and also the assent of the " ordinary member " of the fund, to whom I have referred above, to the remedies put forward.

In the discussion that followed the reading of a paper before the Institute of Actuaries Students’ Society, by E. A. Woodall on the valuation of special policies, F. Bedford explained that certain classes, such as joint life endowment assurances, could be valued conveniently by assuming that all the policies will mature at the same age, and calculating the net premium on the same assumption. This method is mentioned in the Students’ Journal, vol. I, No. 2, pp. 24–26, where Mr. Woodall, in giving the method in the abstract of his paper and the discussion, explains how the method applies to certain classes, and writes : “Since the reserve for an endowment assurance maturing at “70 or 75 is practically the same as the reserve for an endowment “assurance of the same term maturing at 50, 55, 60, or 65, the “error of 10 years in the equivalent age is of little importance,” “provided the net premium is calculated on the same assumptions.” This quotation may be taken as the text for the present paper, which discusses the application of the method to ordinary endowment assurances and the errors involved in its use.