These remarks were set down in 1958 before the Insurance Companies Act 1958 was enacted. The new Act is a consolidating Act and, apart from a few alterations to achieve greater clarity, makes no alteration to the law as it affects Life Assurance business.

The new Act does not, however, include the former Schedules 1 to 5 of the Assurance Companies Act 1909 but leaves the Board of Trade to prescribe them. (Reference is made in these remarks to the powers previously available to the Board of Trade.) The Act required the Board of Trade to prescribe appropriate Schedules without delay and, in fact, the original 1909 Act Schedules have been prescribed without change.

It is understood that this is essentially a temporary measure, as the time available was not sufficient to allow adequate consideration to be given to any possible changes. It is, however, expected that the Schedules will be revised in the relatively near future.

Just over four years ago I had the pleasure of presenting a paper to the Students' Society on some aspects of non-life insurance (J.S.S.13, 139) and I would first like to thank the Society for again giving me an opportunity of putting on paper some further ideas which have largely flowed from my interests in the non-life field. Frankly this paper is of an exploratory nature and suffers from all the defects of reporting continuing experimental work. I hope therefore that the many obvious loose ends will be viewed in this light and that members will be able to sense the excitement of this relatively undeveloped field.

The purpose of this paper is not to provide a guide through the various papers that have appeared relating to the three related topics of retention, reinsurance and risk but rather to provide an elementary approach to these problems with the object of stimulating interest in some aspects of actuarial practice which are largely regarded as lying in the realm of ‘experience judgment’ but which are capable of precise formulation against a background of mathematical statistics.

The word ‘switch’ has come to be used to describe a variety of operations in connexion with pension schemes. A scheme may be ‘switched’ from one life office to another; a scheme may be ‘switched’ from without-profits to with-profits; or the two operations may be combined. This paper attempts to deal, however, with an operation which is the direct result of the Finance Act 1956—the switching of a scheme approved under Section 388(1) of the Income Tax Act 1952 to a scheme approved under Section 379 of the same Act—and it is assumed that the operation takes place within the one life office.

The operation in question has its origin in the somewhat detached view of life taken by our legislators and by the administrators whose duty it is to advise them.

Given any probability distribution, new distributions can be derived from it by assuming its parameters to follow some specific probability distributions. A simple example of this process is provided by the Poisson distribution

P(r∣λ) = e-λλr/r! (r = o, 1, 2, …).

If the parameter λ is assumed to follow the Pearson's Type III law

then the probability of r successes is obtained as

Conjectural estimates of the early population of Britain are subject to wide margins of error. Professor Grahame Clark (1957) has put forward tentative figures of early prehistoric numbers, based upon the native population density in newly colonized lands. The Upper Palaeolithic population density of Britain was compared to that of Alaska in 1867 and the North-West Territories in 1911, and the Mesolithic to that of Tasmania. Since prehistory has no specific dates, being measured in periods of hundreds or even thousands of years, overall numbers must be similarly imprecise in date. Again, the colonial figures themselves are only estimates (the two Palaeolithic estimators being in the ratio 20:3), so that the estimates of prehistoric population might not even be of the correct order of magnitude.

Estimates of between a half and one and a half million have been made for the population of Roman Britain in the second century A.D., based upon different interpretations of the evidence for population density of town and country (Wheeler, 1930). Here we have agreement on the order of magnitude, but the estimates are still imprecise in date and size.