The problem of solvency in insurance is at present under a good deal of discussion in various interested quarters, both national and international. It is principally a question of finding criteria for determining the size of the solvency margin which a private insurer must have in the form of free reserves to be considered solvent. A criterion must produce a margin which is both sufficient and suitable: it must be valid not only for a model portfolio but for any portfolio. Consequently, only insurers with the prescribed margin would be considered solvent and authorized to write insurance business. In recent years, particularly because of the directives promulgated by the Common Market authorities, it has largely been a question of the solvency of non-life insurers.

We now pass to the traces of the early practice of LIFE INSURANCE, a subject which has in general been but very slightly noticed.

The estimation of the value of human life in its rudest approximation—that is, of the term of years which, on the average of a sufficient number of observations, would be observed to fall to the share of each of a given number of individuals born under certain circumstances, and continuing in certain climates or ranks—was to all appearance a subject the consideration of which, not only the speculations of the remoter ages had no impelling cause to enter upon, but one which, if pursued, would have led not only to scepticism, but even to persecution, for entering on a tacitly admitted forbidden ground.

Although this paper deals with the application of mathematical formulae to mortality data, it is not concerned with ‘graduation’ if that word is held to imply the fitting of a particular curve to a particular experience with the object of satisfying statistical tests. Nor is the paper concerned with the development of any philosophical theory of mortality. The experiments which it describes were undertaken in the hope of finding a standard type of curve which would give a good over-all representation of adult mortality in general. If such a curve could be found, an examination of the variations in its parameters might contribute something to an understanding, not of the nature of mortality itself, but of the differences—more particularly the secular differences—between one mortality experience and another.

The various Pension Funds which have been established in the Presidencies of India in the Military, Medical, and Civil Services of the late Honourable East India Company have afforded the means of bringing together a great variety of interesting facts relating to the rates of mortality and marriage amongst Europeans in India. They were originally founded as mutual charitable schemes, giving assistance or pensions to the widows or children of such Members of the services as had not left sufficient pecuniary means for the support of their families or for putting them forward in life. The Company saw fit to encourage these laudable designs by allowing high rates of interest on their invested Funds, and making favourable arrangements in the exchanges for payments to be made in England.

The strict analogy which exists between these two classes of annuities has doubtless received the consideration of the majority of students, but I am not aware that it has ever in print had that attention which it deserves; and at any rate our usual text books hardly even refer to it. Although it is shown, in the short but suggestive article of the late Prof. De Morgan (vol. iv, p. 277), in the most general way, that years, or periods of time, may be interchanged with any other kind of status whatsoever, whether certain or contingent; yet, as successive statuses are almost exclusively spoken of, the less complex cases are liable to escape notice. Under these circumstances, the following brief notes may not be thought superfluous.

With the financial services industries in the member countries of the European Union coming under increasing attention resulting in relaxation of cross border controls, this paper addresses some pensions matters in this European context and how they may relate to the U.K. The main theme of the paper is the book reserve approach to pensions provision. Details of the German book reserve method are provided before developing possible ways in which this philosophy could be introduced into the U.K. These possibilities are assessed and consideration given to the effect they may have on the economy, commerce, the pension fund industry and, not least, the actuarial profession in the U.K.

The title of this lecture was chosen over a year ago before I had formed a clear picture of its scope. It is, however, adequately descriptive of my purpose which is to develop consistent general principles, as opposed to detailed methods, which can serve as a guide to the individual computer—primarily one working alone with an ordinary calculating machine. I shall endeavour to illustrate the principles by actual examples, but it will be outside my present compass to concentrate upon those methods which rely upon brilliance of technique rather than on soundness of principle.

It is clearly desirable to say precisely what ‘computation’ embraces, and I therefore put forward the following definitions of ‘calculation’ and ‘computation’—in each case it being understood that the word is prefixed by ‘numerical’:

Calculation is the application of the four rules of arithmetic to the numerical evaluation of an algebraic expression.

The presentation in November 1905, of three papers on “methods of valuation with allowance for selection” (J.I.A., vol. xl, pp. 1, 15, 42) might well be considered to have left room for no further word on the subject. Any attempt to produce a new method merely to achieve an equal degree of accuracy would undoubtedly be presumptuous, for Mr. King's method affords absolute accuracy, Mr. Diver follows with a microscopic error of £9 on a reserve of more than £3,000,000, and Mr. Ackland closes the series with a larger but still relatively insignificant error of £1,183 on a total reserve of upwards of £13,500,000. It is also shown that in both Messrs. Ackland's and Diver's methods, the error may be expected to be always less than ·01 per-cent.

The practical application of all three methods involves, however, a departure from the familiar system of classifying whole-life assurances according to attained ages, with the loss of all the advantages attaching to that system. This will be viewed by many with regret, and was especially referred to by Mr. Lidstone and Mr. R. P. Hardy in the subsequent discussion. Their remarks, together with Mr. Ackland's cordial expression of goodwill to “other workers in this field” led me to consider the subject from the standpoint of a grouping according to attained ages without any sub-grouping according to duration.

The President of the Institute of Actuaries was in the Chair. The opener prefaced his formal remarks as follows:

I would first of all like to say how pleased and honoured I feel to have been asked once again to take a part in the proceedings of this Society, particularly as this must be regarded as a special occasion since we are honoured by the presence in the chair of you, Sir, the President of the Institute, and also because this meeting is in the nature of an experiment.

It may be within your recollection, Sir, that on the first occasion, some thirty years ago, when I was asked to take part it was also an experiment. We met at the Old Bell and my part was in what has come to be known as Heath's play. It was therefore not so much a surprise to me, as it might have been to some, when three or four months ago the Chairman of the Society telephoned me and asked me to take part in another experiment, mentioning a symposium. Being one of those who dodged compulsory Greek in my undergraduate days I temporized. I consulted a Pocket Oxford Dictionary and found that my memory had not let me down: ‘symposium = a Greek drinking party’. Pursuing the matter further, I consulted the larger edition: ‘symposium = a drinking party, a convivial meeting for drinking and conversation’, and the only example it gives of the use of the word, ‘our symposium at the King's Head broke up, 1787’. This seemed conclusive and, remembering the symposia I had enjoyed with Alan Gardner in the past, I agreed to come along. I was a little disturbed when I received the notice of meeting which mentions a review, but I concluded this was just a printer's error for revue, although I thought the title unusual. My doubts were quite set at rest on Monday when you yourself announced in this Hall that the Society would meet tonight for a symposium.

The paper concerns the situation in which an evaluation of outstanding claims is discounted, in anticipation of investment return earned by the funds supporting that liability. Factors bearing upon the choice of an appropriate rate of return to be assumed in this evaluation are considered.

The ‘standard approach’ to this problem is criticized in two main respects:

(i) there is usually no statement (indeed, no consideration) of whether the discounted value of outstanding claims is to be associated with assets at book, market, or some other value;

(ii) the discounting of outstanding claims is often performed by means of an assumed ‘inflation gap’, i.e. an assumed difference between future rates of inflation and investment return.

Various other matters germane to the determination of an appropriate rate of investment return are listed in Section 2.

Sections 3 and 5 deal particularly with points (i) and (ii) raised above. It is suggested that, in certain circumstances, an evaluation of outstanding claims which fails to address (i) or is carried out on an ‘inflation gap’ basis will be virtually meaningless.

Section 4 deals with the case of an insurance fund in which assets are matched with technical liabilities by amount and term. The considerations which would cause the rate of investment return projected in these circumstances, to differ from that projected in the case of an absence of matching are discussed.

Section 6 deals with the issue of exactly which assets are to be regarded as supporting the liability for outstanding claims. It is apparent that the identification of such assets will affect the rate of return to be regarded as referable to outstanding claims. Particular matters considered include:

(i) assets to be associated with acquisition of new business (and hence not with outstanding claims);

(ii) debtor and creditor items. particularly outstanding premiums and inwards loans.

Section 7 gives a numerical example of the projection of future rates of investment return. This is done by means of a computer projection of various items of a hypothetical insurance fund, taking into account projected future:

(i) interest rates;

(ii) rate of growth of new premium;

(iii) the required distribution of assets by sector;

(iv) profitability of business underwritten.

Conclusions on the various matters considered are dotted through the paper. For convenience, they are collected together in Section 8.

ALL the methods of group valuation submitted to the Institute in the last decade require the calculation of the second sum of the quantities valued, whether in the form of multiplications by —4½, —3½, … 3½, 4½, i.e., the second sum about the centre, or the more convenient second sum about the end. The object of this paper is to show that the α, β method can be transformed so as to avoid this difficulty.