Although much has been written in recent years on the comparative merits of different methods of valuation, I am not aware that any attempt has yet been made to ascertain the ultimate bearing on the Pure Premium Method, of the facts that have been recently brought forward as to the pressure of the expenses and the effects of selection in an assurance company. Speaking generally, it will, I think, be found that proposals to diminish the pure premium reserve on account of the necessarily heavy expenses of new business, have been made without reference to the mortality profit that may be expected to arise from the recent selection of the lives, and vice versa. This being the case, it occurred to me that it might be of considerable practical interest to make an investigation in which effect would be given to the influence both of expenses and of selection, for it would enable us to estimate how far the one neutralized the other. In order to render the inquiry more clear, however, it will be well to begin by considering each separately.

1.1. Consider the situation where a party, in return for a capital outflow of c at a given time (which will be taken as the time-origin), is entitled to subsequent cash flow. This subsequent cash flow may contain positive and/or negative elements of inflow.

Mr. G. F. Hardy has contributed a valuable paper on this subject (J.I.A., xxiv, p. 95) and (p. 103) has done good service by introducing a theorem by Gauss for the accurate integration of algebraic functions limited to any stated degree, and by showing how the same may be applied to the approximate integration of other functions. Again, Mr. George King (J.I.A., p. 276) has made good use of one of the best of Mr, Hardy's formulas in his Numerical Calculation of the Values of Complex Benefits, practically elucidating the important advantages gained by its adoption. I have read these papers with much interest and have thereby been induced to investigate the matter still further, from my own point of view, in its especial relation to assurance calculations, and with results that may be considered worthy of communication.

This subject has been so ably treated by Mr. Sang, in the paper transferred by Mr. Thomson’s permission to the pages of this Magazine, that it might seem almost superfluous to revert to it. Nevertheless, there are considerations connected with it which I believe to be of some importance, and which that gentleman has not adverted to; and I am therefore induced to submit the following remarks, by way of pendant to his observations :—

Many years having elapsed since the Eagle Insurance Company first undertook to issue policies of assurance upon unsound lives, and some doubts having arisen as to the way in which the funds of the Society had been affected by such transactions, the Directors decided that a thorough investigation should be made into the business connected therewith, with the view of obtaining not only a record of the past, but also, if possible, of establishing a guide for the future, and I now have the pleasure, with their permission, of making public the results of that investigation.

It might at first be thought that this paper is limited to the problems of those few who hope to establish a new office in a highly organized and competitive life assurance market. Yet all offices wishing to expand will be faced with problems of a similar nature. This is evident when contemplating a development overseas and was the subject of a paper to the Faculty in March 1960 by R. G. Mallett (T.F.A.26, 547).

The new investigation which is the subject of the present report relates to the experience of the years 1900-1920. The observations include the lives on which all Government life annuities have been granted, the experience under Savings Bank annuities being brought under examination for the first time. The experience under the two classes of annuities, which may for convenience be termed, respectively, National Debt Annuities and Savings Bank Annuities, has been separately investigated, and the broad results elicited are shown separately below.

It may well seem an act of no small temerity to attempt a fresh paper on a subject so often and so ably treated in essays read before this Institute as that of the net premium method of valuation. I am fully conscious of this, and the more so that I cannot profess to be able to add anything appreciable to what has already been said, either expressly or by implication, upon the matter. It will be admitted, however, that the practical importance of the subject, its vital bearing upon the conduct of the business of life assurance, can scarcely be exaggerated. Mr. J. Hill Williams, commenting upon Mr. A. H. Bailey's paper on “The Pure Premium Method of Valuation”, in March 1878 (J.I.A., xxi,, 126), said “The subject of this paper is one upon “which we can never have too much writing or too much “discussion, for it is the very life of our science, and upon the “views which we take of this most important question depends “the safety of many of the greatest financial institutions in the “country”; and with the spirit of such remarks we shall probably all agree. That being so, I think I am right in saying further that we have had no express discussion of this topic at our Institute for several years past. It has, doubtless, on many occasions been referred to—as a thing so intimately intertwined with our daily practice could hardly help being—in connection with other matters primarily before us; but it has not been the actual and avowed theme for consideration.

At the beginning of 1948 the Continuous Mortality Investigation was extended to pensioners who had retired under life office pension schemes. Thirty offices agreed to contribute data, which for the most part are derived from pension schemes issued as “group” business although data for pension schemes operated by means of individual contracts are also included.