This quotation is from the first of that long series of letters addressed to the Registrar General on the Causes of Death in England. Dr Farr was in 1839 appointed ‘Compiler of Abstracts’ in the newly created General Register Office. The saving of 30,000 deaths a year represented about 10% of the current number of deaths. It took some forty years to make that reduction in the death rate, which coincided with Dr Farr's career with the General Register Office.

In the twenty-year period 1936–38 to 1956–58 the Standardized Mortality Ratio for England and Wales fell by 21 % for males and 31 % for females. Measured from a much lower rate of mortality, the rate of improvement has been from four to six times greater than in Farr's day. What of the future?

The basis of this Paper is the new method of graduation introduced by Professor E. T. Whittaker, and expressed in the equation

where δ indicates central differencing, so that δ6u′x=Δ6u′x−3;u′=the graduated and u the ungraduated values of a series of observations, and ∈ is a measure of the importance assigned in any particular case to adherence to the original data as against perfect smoothness in the graduated curve.

Certain terminal conditions attach to this equation, and it is suggested that if no attempt be made to carry the method to the extremes of the series of data, these terminal conditions may be disregarded.

By methods described in the Paper, different summation formulae of graduation are derived from the equation, giving ε various values. The results of test graduations of the a(f) and a(m) ultimate tables by certain of these formulae are shown, and compared with the results under the exact solutions obtained by Dr. A. C. Aitken. A graduation is also made of the Female Government Annuitants 1900-1920 Experience, and the results are compared with these produced by the methods suggested in Dr. Buchanan's recent paper (T.F.A., x., p. 289), and in the discussion thereon.

It is suggested that ε will prove of practical value as an aid to the selection and classification of graduation formulae, and that summation formulae obtained by the methods described have thus a practical advantage as well as one of theory.

Although two papers on industrial assurance by K. J. Britt (T.F.A.21, 265 and 26, 200) have been submitted to the Faculty of Actuaries in recent years there have been no similar discussions of this business at Institute sessional meetings. In addition, papers by G. W. E. Allaway (J.S.S.13, 1) and by K. F. Gardner (J.S.S.13, 22) have been published by the Students' Society, but in none of these papers have the particular problems of collecting friendly societies been fully considered. The industrial assurance funds of societies represent approximately one-fifth of all such funds in this country, and this paper is therefore intended to be complementary to those above-mentioned, to introduce current actuarial problems of collecting friendly societies, and to provide a vehicle for general discussion of industrial assurance.

The level of benefits paid to members of occupational superannuation schemes will depend on the level of contributions made by the employer and employee, the investment earnings received by the accumulated assets and the expenses incurred in the management of the scheme. However, this third factor has been ignored by previous studies into occupational superannuation, even though higher expense levels will naturally cause reduced benefits for a given level of contributions and investment return. In this respect, cost efficiency within the superannuation industry is an important criterion in assessing the efficacy of employer-sponsored occupational superannuation.

The new investigation which is the subject of the present report relates to the experience of the years 1900-1920. The observations include the lives on which all Government life annuities have been granted, the experience under Savings Bank annuities being brought under examination for the first time. The experience under the two classes of annuities, which may for convenience be termed, respectively, National Debt Annuities and Savings Bank Annuities, has been separately investigated, and the broad results elicited are shown separately below.

Dynamic programming, a mathematical field that has grown up in the past few years, is recognized in the U.S.A. as an important new research tool. However, in other countries, little interest has as yet been taken in the subject, nor has much research been performed. The objective of this paper is to give an expository introduction to the field, and give an indication of the variety of actual and possible areas of application, including actuarial theory.

In the last decade a large amount of research has been performed by a small body of mathematicians, most of them members of the staff of the RAND Corporation, in the field of multi-stage decision processes, and during this time the theory and practice of the art have experienced great advances. The leading force in these advances has been Richard Bellman, whose contributions to the subject, which he has entitled Dynamic Programming [1], have had effects not only in immediate fields of application but also in general mathematical theory; for example, the calculus of variations (see chapter IX of [1]), and linear programming (chapter VI).

In 1900 life expectancy at birth in the UK was only 46 years for men and 53 years for women. Just over a century later life expectancy at birth has increased by around 30 years and by 2007 had reached 77.5 years for men and 81.7 years for women. The population aged 85 years and over, often termed the ‘oldest old’, are now the fastest growing section of our population. For the 1921 cohort only 18% of men and a third of women reached the age of 85 years but for the 1951 birth cohort it is expected that almost half of men and 60% of women will achieve that age. The important question for health care planners and society is whether the large number of those who will reach 85 years in the future are similar in health characteristics to those attaining 85 years now.

This question was addressed by substantive results and by methodological papers in the ‘Cohort’ theme of the Joining Forces on Mortality and Longevity conference in October 2009. Here we provide an overview of the papers, some of which are presented in full in this issue (see Murphy (2009), Di Cesare & Murphy (2009), O'Connell & Dunstan (2009), Forfar (2009)).

1.1. Consider the situation where a party, in return for a capital outflow of c at a given time (which will be taken as the time-origin), is entitled to subsequent cash flow. This subsequent cash flow may contain positive and/or negative elements of inflow.

It may well seem an act of no small temerity to attempt a fresh paper on a subject so often and so ably treated in essays read before this Institute as that of the net premium method of valuation. I am fully conscious of this, and the more so that I cannot profess to be able to add anything appreciable to what has already been said, either expressly or by implication, upon the matter. It will be admitted, however, that the practical importance of the subject, its vital bearing upon the conduct of the business of life assurance, can scarcely be exaggerated. Mr. J. Hill Williams, commenting upon Mr. A. H. Bailey's paper on “The Pure Premium Method of Valuation”, in March 1878 (J.I.A., xxi,, 126), said “The subject of this paper is one upon “which we can never have too much writing or too much “discussion, for it is the very life of our science, and upon the “views which we take of this most important question depends “the safety of many of the greatest financial institutions in the “country”; and with the spirit of such remarks we shall probably all agree. That being so, I think I am right in saying further that we have had no express discussion of this topic at our Institute for several years past. It has, doubtless, on many occasions been referred to—as a thing so intimately intertwined with our daily practice could hardly help being—in connection with other matters primarily before us; but it has not been the actual and avowed theme for consideration.

1.1 The price of a particular ordinary share represents an equilibrium position between the views of those participants in the market who wish to buy and those who wish to sell. Most participants, and certainly all institutional investors, have access to a vast amount of background information, and share prices adjust continuously as these participants revise their buying or selling prices in the light of new information or in the light of a changed interpretation of existing information. If an explicit price model can be developed solely from the principle that prices are in equilibrium once all participants in the market have acted on their interpretation of the information available to them, this model will be of considerable assistance in the management of ordinary share portfolios.

1.2 This paper describes the construction and application of such a price model and discusses the optimal extent to which mathematical and statistical methods can be employed in portfolio management. A recent paper by Clarkson (1980) describes the stage of development that had been reached at the end of 1978; the present paper expands on the underlying concept of market equilibrium and on the practical implications for the management of institutional portfolios of ordinary shares.

Continuing process of updating company classifications.

Ninety-six constituents deleted during 1990—many as a result of strengthened casualty rule. Only 74 replaced—reflecting difficulty in finding suitable new non-industrial constituents.

Agencies, Overseas Traders and Publishing & Printing groups discontinued at the end of the year, but Business Services, Electricity and Media introduced. Leisure renamed Hotels & Leisure.