The purpose of this article is to explore the application of computers to actuarial science. It is frankly a propaganda attempt to counterbalance the emphasis on data-processing applications which there has been in the past.

I think that this emphasis has been an unfortunate mistake. Computers can be regarded as glorified desk calculators or high-speed punched-card machinery but this misses the real potential of the qualitative difference between computers and earlier machinery. This potential can only be realized when we learn to look at jobs ‘computer-wise’. There is only one way to learn this and that is to learn how to programme and then to get down to some hard detail.

1. A mortgage is defined as ‘a conditional conveyance of, or lien upon, land or other property as security for the performance of some condition, as the payment of money, becoming void on the performance of the condition’.

2. The emphasis is on ‘the performance of some condition’, and it is with this aspect that the lender is mainly concerned. The ‘payment of money’ will include interest on the amount advanced and repayment of principal by an agreed method—the latter by paying the premiums on a suitable policy, where the majority of new life office mortgages are concerned.

1. S. Benjamin (J.S.S.17, 93) advocates a re-examination of actuarial methods with a view to taking advantage of the capabilities of electronic computers. A somewhat specialized field of actuarial work where such a re-examination is profitable is mortality graduation by means of curve fitting. This field is a specialized one because, in practical actuarial work, graduation can usually be done adequately by straightforward means—for example, a graphic graduation of withdrawal rates for a pension scheme valuation. Full-scale curve fitting is usually reserved for the graduation of assured lives mortality experiences.

Permanent sickness insurance was last discussed by this Society in 1952 when K. Medin submitted a paper on some of the theoretical aspects relating to this class of business (J.S.S.11, 76). At that time only a handful of offices transacted this insurance in this country and of these some did not seem to actively pursue the business. Since then its value, both in conjunction with a life assurance policy and as a separate contract, has become far more widely recognized and I therefore hope that a brief look at the practical considerations involved may be of general interest.

The name ‘permanent sickness insurance’ is possibly misleading. The insurance provides an income during total incapacity, terminating at an age chosen by the insured when the insurance is effected. It cannot be cancelled by the office solely on the grounds of an adverse claims experience. Accidents, provided they are not deliberately self-inflicted or excluded specifically by the policy conditions, are covered.

When the word statistics is used in connexion with non-life insurance the first reaction of most of those concerned with the day-today requirements of the business is to think in terms of the relationship between premiums and claims. In my talk tonight I shall not be concerned with this aspect but will be concerned with the structure of the risk processes underlying the business. In order to try to bring out some of the essential characteristics I have used the minimum of mathematics, using numerical examples to illustrate the points. Furthermore, in order to limit my talk to a reasonable time and to make it ‘live’ I have deliberately omitted many of the finer points which arise in practice to which regard must be had in using mathematical or statistical models to describe the actual situation.

At rock bottom the insurance industry rests on the operation of laws of chance. A hazard is recognized as being liable to give rise to a potential pecuniary liability, and in no time at all someone is prepared to provide a policy against such liability. In devising the policy, and in assessing the rate of premium to be charged, it is necessary to define the event which must happen before a claim can be admitted under the policy and to be satisfied that the happening of the event is fortuitous as far as the proposer is concerned. In life insurance difficulty seldom arises under either count but in non-life insurance the position is frequently very troublesome.

In their text book, The Practice of Life Assurance, published in 1952, Coe and Ogborn devoted less than four pages to the methods of calculating premiums for varying temporary assurances, including family income policies. At that time decreasing temporary assurances were relatively uncommon except for a block of single-premium policies transacted mainly by a small number of offices which specialized in them.

Since that date, however, the transaction of this type of policy on an annual-premium basis has assumed very substantial proportions, particularly in connexion with mortgages, and the cover provided varies considerably among different offices. Some are prepared to go to considerable lengths to provide exact cover, whereas others appear reluctant to go into any great refinements. This is understandable as the calculation of premium rates is quite a formidable task whichever of the known methods is used. The not infrequent changes in building societies' interest rates add considerably to the difficulties.

At the Annual General Meeting of the Students' Society in 1961, a motion was passed that articles of a less serious nature than those normally published in the past be accepted by the Editors of J.S.S. It is in the spirit of this motion that this article is offered. It does not pretend to advance actuarial science in any way, and its only purpose is to introduce members of the profession to a technique which is interesting in that it is different from our normal techniques and to show that it has possibilities in the actuarial field by demonstrating its applications in other fields.

This is not the first time that the subject has been written about in an actuarial journal. Edmund C. Berkeley (1937) wrote a paper for the American Institute of Actuaries going into the subject in some detail, and it is from this paper that I have taken my examples of applications to life office practice.

1. The purpose of this paper is to consider procedures involved and the records and documents required after a life proposal has been accepted. It is mainly concerned with a particular office using a punched card system, the changes which have taken place and the further changes in prospect as other office machinery is brought into use.

In particular, the use of automatic typewriters for the production of policy and other documents is examined.

In the office concerned there has been a rapid expansion both in quantity of business and diversity in type of business. The tendency has been for a multiplicity of records to be built up for reference purposes and to control the Powers punched cards used for premium collection, valuation, etc. Energetic attempts have been made from time to time to reduce the work involved in setting up, housing, and accurately maintaining these records.

In February 1957, R. G. Mallett presented a paper on behalf of four South African actuaries entitled ‘The Actuary in South Africa” (J.S.S.14, 4). The object of this paper is to describe some of the developments in South Africa since that paper was presented, and also to describe briefly the conditions and the problems with which actuaries have to deal in the Federation of Rhodesia and Nyasaland and in the East African territories Kenya, Uganda and Tanganyika. The majority of actuaries working in South Africa are concerned in some way with the administration of business in these countries, as are actuaries of British companies which operate there either direct from the United Kingdom or through a branch office in Johannesburg or Cape Town.

1.1. The principal field of work in which the actuary is engaged is still that of life assurance, and over the years the tremendous growth of life companies has necessitated the individual actuary specializing in one or other of the various branches of life assurance work. In this paper, the authors, each of whom is intimately concerned with the formation of a new life assurance organization, seek to examine many of the elements affecting a new office, and hope by so doing to present the problems as a whole rather than as the separate compartments in which many practising actuaries find themselves.

1. The level of real earnings in the insurance industry, as in most others, has increased considerably since the end of the war. The problems raised by this fact are of vital interest to the actuary, since the adequacy of his premium scales and the maintenance of bonus rates depend on expenses being contained within reasonable limits. The total amount of agency remuneration may be determined in the long run by forces outside the actuary's control, but he can have considerable influence on its structure. The purpose of this note is to set out the principal methods of remuneration at present in use and to suggest some modifications of the incentive element which might be of advantage to the offices and the policyholders without harming the interests of the agent.

British life offices transacting life assurance outside the United Kingdom have until now confined themselves almost entirely to the countries of the British Commonwealth—because among the countries with stable currencies the members of the Commonwealth have in the main been the ones with which we have had the largest numbers of other business contacts. Another influence has been the absence of a language barrier. Before the 1914–18 War some offices transacted business on the Continent of Europe but thereafter most of them pulled out; today as far as I know only one British office transacts life assurance in France, one in Germany and none in Italy.

One might be forgiven therefore for thinking that actuaries handling life office affairs need not concern themselves with life business on the Continent of Europe—particularly as, at the beginning of last year, the negotiations for Britain's entry into the European Common Market broke down.

In October 1961, the author wrote the editors a letter which was subsequently published (J.S.S.16, 481) urging the submission of articles which were only germs of ideas. Part of what follows has arisen out of earlier research, and part falls into the ‘germ’ category in the hope that it might give rise to future development.

Ever since the days when Makeham‘s formula appeared to have ceased to fit most mortality experiences, some actuaries have striven to find an ideal formula to take its place, and perhaps others have been interested. Even if such a formula were found, it might only be a matter of a short time before the shape of the mortality curve changes in such a way as to render that formula out-of-date too; but that is no reason for not continuing to strive.

This paper is concerned primarily with the principles underlying the planning of retirement and death benefits for the employees of an international organization. The development of pension systems throughout the world is so diverse that it would scarcely be practicable within the limits of digestibility to present a comprehensive factual survey and no attempt is made to do so. The paper is confined strictly to a consideration of benefits payable at normal retirement age or on death, and ancillary benefits such as invalidity pensions are not discussed, except for occasional references when survivor and invalidity benefits are closely linked.

At the present time the non-life side of the insurance industry is faced with many difficult problems. The poor results often shown by motor insurance accounts are bringing many insurance men to the conclusion that it is virtually impossible to conduct the business on a sound basis and that they must regard it as an onerous public service. Fire insurance business, for so long the backbone of many general insurance accounts, has caused increasing concern in recent years as the national level of fire wastage and the proportion of large fires have continued to increase. It seems worth while therefore, to ask whether the statistician can help to solve some of the problems of transacting non-life insurance in these circumstances. In this paper the author draws on three years' experience of research into the statistical aspects of general insurance to paint a broad picture of a scene unfamiliar to most actuaries. It is hoped that attention is thereby drawn to the potential value in this context of the techniques of probability and mathematical statistics.

1. The S.A. 56/58 Ultimate data (see J.I.A. Vol. 87, p. 371) was originally graduated by summation formula and arising out of the discussions it was decided to attempt to fit a mathematical formula of the Perks type.

2. To start with, data below age 30 were excluded.

3. The generalized Perks formula

was chosen—the thought being that if some of the parameters were not needed the process of curve fitting would result in these parameters assuming small values.

In this paper, the main object of which is to promote a mutually helpful discussion, a deliberate attempt has been made to avoid going into detailed descriptions of methods of administration. These vary, of course, from office to office and it is quite reasonable that the difficulties which presented themselves should have been successfully surmounted in different ways. It is both interesting and informative to learn the various practices which have been adopted, but a close study of them may lead to an oversight of underlying problems and a disproportionate expenditure of time.

It should also be mentioned that the title would be really more suitable for a whole book rather than for a short paper presented for a single evening's discussion. Consequently, two restraints have been imposed, both of which derive from the dynamic growth in size and complexity of group pension business over the last two or three decades.