When invited to prepare a paper to the Students' Society I had in mind selecting a topic from each of the various branches to illustrate the types of problems that are inherent in non-life business. However, as my ideas took positive shape, I found myself drawn into a more active study of certain aspects which have received little attention in this country, although some considerable theoretical and a limited amount of practical work has been done on the Continent. Instead, therefore, of giving a general description of various features I have largely limited myself to techniques which could be used in practical application and thus endeavoured to bring into relief some problems which indicate the almost unlimited scope for practical and theoretical investigations.

2. Initially the treatment is simplified; I hope that I have succeeded in picking out the spots where intuition rather than formal proof has been my guide, but if I have not I hope my critics will give me latitude in this exploration into largely unexplored territory.

Chiefly, perhaps, owing to the increase in the average size of our industrial or other organizations and to the increased facilities for carrying out the work by punched-card and other office machinery, there has of recent years been an increase in the country generally in the use of a number of organizational or management techniques of an analytical or statistical character. The tendency is more marked in America than in Britain, but even here we find an increased use of such techniques as ‘Market Research’, ‘Sales Forecast’, ‘Cost Analysis’, etc.

The more this type of statistical analysis finds favour, the greater will be the demand for increased statistical data relating to the economy of the country or of its social structure. Mr John Ryan, Vice-Chairman of the Metal Box Company Ltd, made this the main subject of his Alfred Watson Memorial Lecture to the Institute of Actuaries on 24 March 1952.

A brief, introductory talk on a subject, such as this, will naturally be expected to start with a definition. In this, I must frankly admit to some difficulty, as I do not know of any really satisfactory definition of operational research. This, however, is nothing to be abashed at. It is usually easy enough to be clear about a field of study when you are in the centre of it; the boundaries, however, are commonly diffuse—and it is with boundaries that definitions are concerned. This difficulty of precise definition can be found even with quite well-established fields such as physics or, dare I suggest, the actuarial profession.

I shall therefore be content to quote a phrase which is commonly applied to operational research, really more a description than a definition, and shall then try to expand and explain the salient points incorporated in it.

Lidstone has shown that the solution to the theoretical problem of valuing a life interest is essentially indeterminate. For a uniform life interest this is generally avoided by requiring of the formula that at the end of any policy-year the purchaser will have received sufficient income to discharge all premiums to date on the supporting policy, and to provide the predetermined interest on his total outlay.

Consider a life interest to be valued of 1 per annum, and let P be the office rate of premium on the whole-life non-profit policy required to return to the purchaser his initial outlay. In the evolution of a formula three unknown quantities are involved:

G, the gross purchase price (including expenses);

T, the total initial outlay;

S, the sum assured.