1.1. The aim of this paper is to initiate a discussion between actuaries, accountants, the Department of Trade and others working in insurance on our basic concepts, language, methods and aims. We need to discuss concepts and to agree on language in order to be able to discuss methods and aims. The concepts and language developed by actuaries in life business are very different from those used in non-life insurance and a synthesis of the two is long overdue.

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.

1.1. This paper is based on the report of a working party set up by the Institute Research Committee and which met for two years from December 1972. The original objectives of the working party were:

(a) to identify current philosophies of bonus distribution in a fund with a high equity content.

(b) to review the methods used for valuing assets and liabilities and the inter-relationship between the respective methods; and to consider the effect of the current philosophies of bonus distribution on those methods.

(c) to investigate methods of valuing assets and liabilities and to carry out research into methods appropriate to modern conditions.

1.2. The working party was not satisfied that it had satisfactorily achieved its objectives but, nevertheless, felt that it should report the progress it had made. The full report is available from the Institute Library together with synopses of some forty papers that were considered relevant. This paper omits the two sections of the report which reviewed current methods of valuation for publication of assets and liabilities and expands other sections in the light of recent events.

The work of science is to substitute facts for appearances and demonstrations for impressions.

1.1 .This paper is an attempt to describe the extent of ‘Subjectivist’ infiltration into theories of actuarial concern, and to present counter arguments defending the objective ‘classical’ actuarial position. The principal entry point for subjectivist ideas has been the ‘latter day rediscovery of the basically statistical nature of actuarial work’ (F. A. Menzler) which has introduced us to Bayesian Statistical Theory and the concept of Insurance Theory as a Theory of Risk. Classical actuarial theory, however, regards this use of Bayesian theory as fallacious, and the Theory of Risk as of relatively minor interest.