The President (Mr M.H. Field, C.B.E.): Tonight we have a double event and so commemorate the names of two distinguished actuaries: John Finlaison, our first President from 1848 to 1860; and Sir Alfred Watson, the first Government Actuary and our President from 1920 to 1922.

In 1985 the Council reviewed the procedures for awarding medals and decided to widen the eligibility of the old Silver Medal and to change its designation to a renamed Finlaison Medal. The Finlaison Medal may be awarded “in recognition of service to the Actuarial Profession in furtherance of one or more of the various objects as set out in the Royal Charter”.

It is a privilege, Mr President, to be invited to lecture to your Institute, especially in commemoration of Alfred Watson who did so much to establish the firm foundations of your profession. These are of such detail and intricacy that you remain elite and hardly subject to the kind of challenges which more and more affect other professions. Perhaps your time will come as mutterings are heard about your valuations of pension funds and to whom they belong.

The subject of this lecture tonight is the way in which risk has forced itself to the front of public discussion and finds the expression in comment almost every day, whether on the issue of vaccine damage to children, medical negligence, the Chernobyl disaster, landslides in Colombia or floods in Bangladesh.

1.1 Medical expenses insurance, as we know it today, has been available in the United Kingdom since the late 1940s. In recent years the market has increased significantly to a point where we estimate approximately 6m people are now covered by medical expenses insurance, which represents over 10% of the population. Furthermore, there is evidence that the market is continuing to expand.

A common method of measuring relative mortality experience in actuarial, demographic and epidemiological studies is by way of comparison of the actual number of deaths and the number expected if a given standard experience were applicable. The properties of this method are discussed. Further ways of making such a comparison are described, one of which (the widely used Cumulative Mortality Ratio) has a serious bias in application to follow-up mortality studies. The properties of an alternative approach, the Ratio of Geometric Average Death Rates (RAD), are also discussed. This extends the analysis published in 1982 by the author, although attention is focused here on ratios that measure relative mortality experience.

It is now some sixteen years since Sir David Cox (1972) published his epoch making paper in which he incorporated regression type arguments into life-table analysis. Central to the method was the introduction of the multiplicative hazard

with vector of covariates z, unknown regression parameters β, and so-called base-line hazard λ*(t) = λ (t, 0). Applications of the method, based on the conditional likelihood argument expounded by Cox in which the base-line hazard λ* is unknown, have proliferated in the intervening years, largely in the field of medical statistics. There have been relatively few applications in which the base-line hazard is assumed known at the outset. Specific cases include Breslow et al. (1983), Berry (1983) and Hill et al. (1985).

When two or more independent or component loans are consolidated to form a single composite loan the result is often referred to as a cocktail loan. In this paper we analyse properties of a composite loan induced by properties of the component loans. Of particular interest are the properties of the composite yield in terms of the yields and other characteristics of the component loans. Some upper and lower bounds are also established for the composite yield in terms of the component yields. Of some importance is a sensitivity analysis of the composite yield with respect to various parameters of the component loans.

J.I.A., 114, Part II

A Linear Approach To Loan and Valuation Problems. By A. Brace, B.A.

On page 395 in the Proof of Theorem 2 replace the first twelve lines by: