1.1. It is traditional for acknowledgments to appear at the end of a paper. However, in this instance the main acknowledgments are due to those who, by their inspiration, made the conception of the paper possible, and cannot be separated from the underlying ideas and the aims and objects, which usually appear near the beginning. I therefore start with a grateful acknowledgment to F. M. Redington whose remark, made in private, that he would love to know the causes from which annuitants do not die, ignited the first spark without which this paper could not have been written; to R. D. Clarke who, when he was Secretary of the Continuous Mortality Investigation Committee, indicated the names of the two life offices who might be able to supply the required information; and to J. H. Gunlake and D. F. Gilley who, in the early stages, provided the necessary encouragement and stimulus to get the project off the ground.

Actuaries tend to use deterministic rather than stochastic methods and confine their calculations to the computation of expectations. The adverse effects of statistical fluctuations are usually avoided by including contingency margins in the calculations and professional judgment plays a large part in the determination of the margins. In this paper, we show how the results of two recent theoretical papers can be used to supplement professional judgment in the area of premium loadings for non-participating business. The methods are also of interest in connection with participating business.