1. In the following experiments I simplify enormously, by assuming that the only benefit provided is a pension on retirement at age 65, that there are no benefits at all on death, not even a return of contributions, and that there are no ill-health retirements or early retirements. I also assume that all salaries, contributions and retirement pensions are paid annually in advance. This simplifies the calculations and hardly affects the results. I also assume complete certainty of inflation. salary increases and investment returns. The purpose of the experiment is to investigate the relationship between the amount of pension that may be deemed to have ‘accrued’ each year, and the amount of contribution (as a percentage of salary) needed to purchase the extra pension that has accrued in each year. under both a final salary defined benefit scheme and a revalued average salary scheme.

The purpose of this paper is to provide an opportunity for discussion within our profession of ‘the use of an actuarial approach and actuarial evidence’ in the assessment of damages arising out of personal injury and fatal accident litigation. The need for such a paper was intimated in the pages of our Journal by William Phillips in his Review of Principles of the Law of Damages by Professor Harry Street. Since the publication of what Phillips described as ‘from the actuarial point of view…the most important legal textbook which has been published in the last 50 years’ the employment of actuaries in this field has been widely discussed within the legal profession. The most important recent development has been the inclusion of personal injury litigation as Item VI of the first programme of the Law Commission set up by the Law Commission Act, 1965. The words quoted in the first sentence above are taken from the list of ‘Questions for Examination’ under (b) of Item VI, ‘Assessment of Damages’. The current examination being conducted by the Law Commission makes this a particularly appropriate time for a sessional meeting on this subject. The writer has had the advantage of a sight of a preliminary Working Paper prepared by the Law Commission and will be quoting certain extracts from that paper below. It must however be stressed that the Working Paper is a preliminary one which attempts to do no more than canvass views: it in no way sets out the conclusions of the Law Commission on the matters discussed.

The subject of valuation is one of the most important, and at the same time most difficult, of all the problems faced by actuaries.

The traditional approach to the subject has centred on discussion of the relative merits of the net premium and bonus reserve methods of valuation, and on the inherent conflict between valuation as a means of demonstrating solvency and valuation as a tool for ensuring a smooth emergence of surplus in accordance with the need to declare uniform reversionary bonuses. This approach is covered in the well-known papers by Redington (2) and Skerman (3) (4) and forms a significant part of the course of reading for examination subject 8 (formerly B2).

Bonus reserve methods are, typically, ‘active’ methods of valuation in which all relevant parameters, including expenses and future bonuses, are given values close to their expected values. The premium valued is the office premium, and assets are usually valued at market value or by discounting expected investment income. Because actual conditions are always changing, an active valuation method tends to lead to frequent changes of basis and this introduces an element of volatility to the results which can, in consequence, be difficult to interpret. Nevertheless, because of the emphasis on using realistic values for all parameters, it is commonly believed that bonus reserve methods are particularly appropriate for investigations into solvency, especially when external conditions are changing rapidly, and in determining appraisal values.

This paper explores the benefits and limitations of a valuation framework as a management tool within a general insurance operation. Two models are presented, one a model of the firm and the other an option valuation model, which together create a robust framework that enables management to analyse how different decisions would affect both the overall firm value and its distribution amongst investors. The model of the firm assists in understanding how key factors such as the momentum of a general insurance portfolio and the allocation of scarce resources affect the value of the firm. The second model, an option framework for corporate liabilities, highlights the critical distinction between the value of the firm and the value of investors' claims on the firm.

Several writers, notably Messrs. Higham and Sprague, have treated of the Mortality Experience of Life Offices, basing their investigations upon various data; and it may be thought that there is no necessity to pursue the subject further. The question is, however, one of great interest and importance, both in its relation to abstract science, and in its bearing on the actuarial management of companies; and as it possesses collateral branches which have hitherto received but little attention, it occurred to me that my time would not be wasted in attempting to elicit new facts, and illustrate old ones, from the abundant materials now at our disposal.

…the solutions given…are so various as to excite no little surprise and distrust in the minds of those unacquainted with the subject, under whose notice such solutions are brought.

…a great deal of judgment and discretion must always be required from the actuary, and…it is not possible to lay down any general rule which shall altogether obviate such requirement.

The quotations above are taken from a paper by Jellicoe (J.I.A.6, 61) which was discussed by this Institute in 1855. It is a salutary thought that there are no subsequent statements recorded in J.I.A. on the subject which seem to express so succinctly the two principal points which should always be borne in mind when the apportionment of a trust fund is under consideration. It must be stated immediately, however, that since 1855 problems of apportionment have been discussed only in 1871 (J.I.A.16, 269), 1873 (J.I.A.18, 77) and 1925 (J.I.A.56, 243); indeed, reversions and life interests have scarcely been mentioned in Institute discussions since 1935, when O. I'A. Thurston presented his paper on Death Duties (J.I.A.66, 369).

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.

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.

The Presidential Address visits some of the current issues affecting the actuarial profession and expresses some personal views of the President. Subjects covered include with-profits policies, life assurance withdrawals and disclosure, Europe, education (concerning both actuarial examinations and continuing professional education), general insurance and pensions. The Address demonstrates the need for proactivity in a world which is continually changing, which is the theme of the 2-year presidency.

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.