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.