This paper is partly descriptive, partly analytical, and covers the following aspects:

a description of the market in general;

a brief description of the organization of Lloyd's;

currencies and exchange rates;

calculation of reserves;

taxation;

underwriting; and

accumulation of risk.

§§ 1 and 2 and the earlier paragraphs of § 3 convey information regarding the market that will be well known to actuaries practising in this field and may be passed over without loss. They are added in an attempt to convey a picture of the type of operation that results within an office concentrating on reinsurance business, as against looking at reinsurance in its peripheral effect on a direct writing office.

1.1. The market in British Government stocks in many ways resembles what might be called a perfect market. In particular, very large amounts can be dealt in, dealing expenses are low, powerful statistical techniques are used to identify price anomalies, and frequent switching operations take place to exploit these anomalies. Given these features, prices of stocks will vary in a highly regular manner, and it should be possible, by the application of graduation methods, to represent the price structure in mathematical terms. If such a descriptive framework can be developed solely from the principle that prices are in equilibrium under the switching action of all participants in the market, it will provide the basis for a mathematical model that could be used for many functions of portfolio management.

1.1. In the past ten years, traditional with-profit endowment assurances have been faced with severe competition from two new products, which offer considerable flexibility to the policyholder combined with certain guarantees not normally available in the traditional endowment policy.

The first of these new products, unit-linked assurance, has been analysed in some depth in recent papers submitted to the Institute, Faculty and Tokyo Congress. In particular, papers by Benjamin, Wilkie and Scott have developed stochastic models that have enabled the premiums and valuation reserves for maturity guarantees under these policies to be quantified with a much greater degree of certainty than had previously been the case.

Every profession should be concerned with the problem of matching training and working practice. The problem is especially a vital one for the small but powerful actuarial profession seeking to adapt to significant changes.

This note gives a brief summary of my Ph.D. thesis, which was based on questionnaires concerning the training of actuaries, and also in § 7 makes reference to a more recent investigation.

A survey was designed and questionnaires despatched in 1973, in an attempt to discover the existing relationship between actuarial training and occupational practice, whether there was any shortcoming in this relationship and if so what might be needed to correct it. The response rate from the 236 actuaries who qualified for the Fellowship of the Institute of Actuaries in the four sets of examinations spanning the two calendar years 1972 and 1973 and who formed the test population was 81% (192 replies).

This paper has been written to present a new approach to the determination of approximate actuarial formulae. The method employed involves using certain desirable conditions to find the values of arbitrary parameters in a general formula. It is considered that the best way to introduce the new method is by example, consisting of applications of the new technique to some practical problems in the theory of compound interest.

More than 200 years ago, on 30 April 1760, Daniel Bernoulli (1766) read a memoir to the Royal Academy of Sciences in Paris entitled Essai d'une nouvelle analyse de la mortalité causée par la petite vérole, et des avantages de l'inoculation pour la prévenir (see Bradley, 1971, for a translation). In this remarkable memoir Bernoulli produced the first double decrement life table and one of the related single decrement tables, as well as deriving a mathematical model of the behaviour of smallpox in a community. This model was the forerunner of considerable developments in the mathematical theory of infectious diseases, a description of which is given in N. T. J. Bailey (1975). During the half century following Bernoulli's memoir there were a number of papers by other authors on the subject of that memoir; these, and the original memoir, seem to be little known to actuaries and are the subject of the present paper. They could have been the starting point of the actuarial development of exposed-to-risk formulae, but in fact were not.