I cannot recall that national fuel policy has ever previously been the subject of a paper to the Institute, though it is becoming quite usual for the Institute to address itself to subjects outside the traditional actuarial fields. Nearly all the Alfred Watson Memorial Lectures, for example, have been on outside subjects and two of these, ‘Some thoughts on economic forecasting’ by Sir Alexander Cairncross (as he is now) and ‘Problems in forecasting in the chemical industry’ by Sir Paul Chambers, have certain links with the subject of this paper.

A review of Opinion No. 8, which is a statement by the American Institute of Certified Public Accountants (A.I.C.P.A.). Opinion No. 8 is of interest to actuaries for the following reasons:

(1) Its history provides a study of the painstaking methods followed in the U.S.A.

(2) Any actuary who becomes concerned with the pension affairs of a subsidiary of a U.S. company will need to know the scope of the Opinion, its requirements and the difficulties to which it may give rise.

(3) The relationship between members of different professions has to be considered from time to time. Opinion No. 8 concerns itself to some extent with actuarial matters, and it is important to be clear about what it purports to do and the precise roles cast for actuaries and accountants in dealing with it.

(4) It is another factor stimulating discussion regarding pension funding methods.

Throughout this century mortality has been declining and if an exponential curve in the Gompertz form μx = bcx is fitted to recent English Life Tables b has been decreasing as we would expect. Between the 1911 Table and the 1951 Table, 105b has fallen from 18 to 6 for males and from 9 to 2 for females. But c has been increasing—from 1·087 to 1·103 for males, and from 1·094 to 1·112 for females. What feature of mortality can it be that has been deteriorating in this scientific age? Has c any counterpart in reality? Or is it just a mathematical by-product of our system of description?

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.

The classical approach to actuarial problems has been deterministic. That is, the assumption has been made that the number of policies in force is large, that chance fluctuations are unimportant, and that the use of mean values is adequate. The actual cost to a company of an annuity, for example, may in fact vary from nothing (if the annuitant dies immediately) to a large amount (if he lives to be a nonogenarian). On average, the cost will be ax, and for many purposes, this value is good enough.

The method of simulation, alternatively known as the Monte Carlo method, to which Sidney Benjamin drew our attention is a lazy way of solving problems that could be solved accurately but for the large number of different logical situations that have to be considered. The method traces out what actually happens if the conditions of a problem are observed and if certain unknown events are presumed to occur at random. The solution is taken to be the average of the results of all the experiments. Inevitably, however, this method gives rise to random error. Now certain actuarial problems depend on making assumptions on such things as the mortality to be expected to be experienced by a life or set of lives. It is of little consequence if random error is imposed on top of such assumptions. On the other hand the shape of the probability distributions that the random variables in the problem are to follow may be known exactly. For such a problem the introduction of random error is a blemish that should be made as small as possible. In this note one such problem will be considered. The argument will introduce the subject of balanced incomplete block designs, which, as far as the writer knows, have only once been touched on by an actuary and that over one hundred years ago. The problem is the chance that a Jackpot may be opened at the game of Poker, discussed by Redish and Ross.