This paper has two functions: first, in part 1, to present briefly the results of some recent investigations into the behaviour of a price index (in the United Kingdom) in order to gain some insight into the possible future progress of inflation; secondly, in parts 2–4, to present the arguments in favour of the linking to a price index of financial instruments, in particular government stocks, life assurance contracts and pension fund benefits. Part 1 is heavily statistical, and those who prefer the controversial material can go straight to part 2, noting only the conclusion to part 1, viz.: that it is not easy to forecast inflation over any lengthy period. Parts 2–4 are controversial, and I expect will still be topical when the paper is presented. I make no pretence to be impartial; I am convinced that widespread index-linking of long-term contracts would have a beneficial effect on the conduct of our financial affairs. It is up to those who disagree with me to put their case in the discussion; but I hope my supporters will express their views too.

1.1 In recent years, the United Kingdom members of the actuarial profession have become increasingly involved in the general insurance industry and therefore the Institute decided that the subject of general insurance should be included in its syllabus from 1977.

1.2 Prior to 1977 there were a number of papers and articles, written for either the General Insurance Study Group or the Research Committee, on various subjects related to general insurance. These papers and articles have not always had a wide circulation, although they have been deposited in the library at Staple Inn.

1.3 Most of these papers were of an explanatory or technical nature. In the authors' opinion, the actuary has a much wider rôle in general insurance than the technical one of estimating the liabilities of claims. In fact, the actuary should be able to provide a blue-print or framework for the financial management of a general insurance company.

1.4 A general insurance company is a financial concern; therefore the actuarial profession should have a rôle to play. In describing the financial concern, the actuary is required to chart the waters linking profitability, solvency, growth, reserving basis, dividend policy and capital requirements. As the second half of this paper will show, these items are inter-linked and decisions on one should not be taken in isolation as they will have repercussions on one or more of the other items.

1.1. The concept of matching assets and liabilities has for many years been recognized as a crucial aspect of our professional work. Its importance is emphasized in the Institute's guidance notes entitled “Actuaries and Long-Term Insurance Business” and in many papers published in the Journal.

1.2. A particular form of matching, namely immunization, was developed by F. M. Redington in his paper “Review of the Principles of Life-Office Valuations” (J.I.A. 78, 286). Immunization signifies the investment of assets in such a way that the existing business is immune to a change in the rate of interest. One of the consequences of immunization is that the mean term of the asset-maturity dates is appreciably longer than the mean term of the value of the asset-proceeds and of the liability-outgo; and, at other than low rates of interest, a perpetuity can be too short to immunize a long-term contractual liability.

This is not so much a paper as a series of loosely-connected essays and it requires explanation.

For some years I have felt that my generation had an unusual duty to the history of the profession. The first 180 years of actuarial history no doubt seemed eventful enough at the time but they took place against a stable background when interest rates were seldom outside the range 3% to 5%. But since 1945, say, a turbulence undreamed of in those earlier days has become the commonplace of our activities.

This problem concerns n couples around a circular table, husbands and wives seated alternately. The number of ways in which the n couples can be seated such that no husband and wife sit next to each other is required. This problem is not covered in the standard texts such as Feller (1950) or Whitworth (1901) who concentrate on the simpler linear problem, i.e. seating arrangements in a row. In this paper we obtain a solution for the circular problem, deriving thereby the probability that no such matching occurs when the seating is made at random, and showing finally that this probability has a limiting value when n is large.

This note continues an annual series on mortality rates in Great Britain; the previous note in the series appeared in J.I.A. 107, 529 and dealt with mortality in 1978. Tables 1 and 2 below show central death-rates for Great Britain for the years from 1966 to 1979 and Tables 3 and 4 show the ratios of these rates to the corresponding average rates for the three years 1970–72, which have been taken as a standard. Death-rates in this form for the years from 1961 to 1978 have been published in earlier notes in this series. The rates for 1979 have been calculated using the deaths recorded as occurring in Great Britain in 1979 and the ‘home’ population at 30 June 1979, i.e. the number of people actually in the country at the time, as estimated by the Registrars General of England and Wales and of Scotland.

Richard Witt's Arithmeticall Questions, published in 1613, was a landmark in the history of compound interest. In a previous paper (J.I.A. 96, 121) I have described the book and attempted to show why it is so important.

This article sets out some information about Witt's life, which has come to light as a result of research done since the previous article (when very little was known about him). Then follows a discussion of some of the books on compound interest which were published later in the seventeenth century. These not only help to fill in the practical background but also show how the techniques came to be more widely known and how problems arose when interest rates were reduced. It is worth noting that there was an average inflation rate of around 1% p.a. during the first half of the century and an average inflation rate of nil, or even a slight deflation, during the second half (Birks & Morrell, 1976; Mitchell & Deane, 1962). Thus, to a very considerable extent, the interest rates used in calculations were real rates of interest.