1. In the past, concepts of funding and methods of costing have frequently been discussed in papers submitted to the Institute and the Students' Society usually with particular emphasis on selfadministered funds. There is still scope for further thought on the subject of funding methods and it is hoped that this paper will provide an opportunity for further discussion with particular reference to insured schemes. Life offices are not in the same position as consulting actuaries since their basic function is to insure the benefits required rather than to give professional advice. At the same time they have a responsibility to ensure that their costing methods are basically sound and that the issues involved are not misrepresented to their prospective and current policyholders. In recent years there has been a tremendous demand for final salary arrangements using the controlled funding system of administration but little attempt has been made to codify the principles which ought to be followed in making cost estimates.

1. In this note we shall try to unravel a puzzle. It is hoped that the triviality of the subject-matter will not persuade the reader that it is unworthy of his attention; our excuse for offering it is that the underlying principle turns out to be applicable to some very practical situations. In many of these we experience no problem and seem to be on firm ground, as may a man who on a winter's day strays from the common on to the pond, until the ice breaks.

2. By repeatedly presenting theorems that appear intuitively to be unacceptable, a mathematical training is apt to engender distrust in the conclusions of common sense. When the mind has learned to convince itself of the truth of a host of astonishing facts, it hesitates to reject a fresh one however improbable it may seem. This reluctance has an unfortunate consequence, in that the more often the validity of such results is demonstrated, the less the urge is felt to scrutinize a new proof before entering yet another black mark upon the long crime sheet of intuition. Thus, paradoxically, the highly trained expert may sometimes be deceived into accepting a false statement that would be instantly denied by a layman incapable of following its supporting argument. ‘You can't fool me’, boasts the novice, ‘I'm too ignorant.’

The subject of reinsurance has received relatively little treatment in our actuarial literature and indeed the definitive paper on the subject was written by G. T. Foster in 1945. This paper is still the recommended reading for the subject in the Final Examination. Non-proportional reinsurance finds its usual place in the fire and accident departments but for reasons which I hope will become apparent later it is much less common in life assurance. It seems to me that the reason for this is that it is a form of cover unattractive to both parties since it is essentially short term, whereas life assurance offices are concerned with long term liabilities. Nevertheless, since some actuaries may be unfamiliar with the subject chosen for this meeting, I felt that the ground might be better prepared if the subject of life assurance were treated first.

Definitions

It is usual to start with a definition and in this case it is easier to define what is meant by proportional reinsurance, since this is the type of reinsurance most commonly encountered by actuaries.

It may be stated as follows: When a claim arises, the shares of the reinsurer and ceding company are paid in proportions which were fixed in advance. This is a simple and rather obvious statement, and for this very reason it is often overlooked.