I Have been asked to explain how the benefits of a pension to widows and an allowance to children can be valued when they are included in a pension scheme; and as I have had no experience whatever of a fund providing such benefits, I am, of course, eminently qualified to lecture on the subject. At least, I approach the subject with an unprejudiced mind, and am not affected by anything I may have said or done.

A feature of modern wars has been the impetus which is given to the development of scientific and technical progress, a phenomenon which is very easily explained by the general urgency of development under the pressure of war requirements, the removal of normal limits on expenditure and the realization of the part that science can play in the development of the engines of war. This was shown to a marked extent in the second world war and amongst the examples can be quoted the vast development of electronic equipment, the emergence of the jet engine as an alternative to the internal combustion engine for motive power and the realization of the use of nuclear power, in the first instance in the form of explosive energy. However, over and above these examples of scientific and technical progress there was one development in the second world war of particular interest, the use of the scientific method of ‘operational research’ (hereafter denoted by O.R.).

1. In this note I describe the mathematical formulation of a model for representing the spread of AIDS in a population, which is designed for actuarial use in dealing with life insurance companies and pension funds. A major requirement of actuaries is that the model should be age-specific, and should take into account normal age-specific mortality as well as the extra sickness and mortality from AIDS.

This discussion paper was produced by a Working Party in April 1997 to put forward some possible ways of improving the United Kingdom financial regulatory process. It was written to contribute to the expected post General Election debate on this topic. Although the new Government announced plans in May 1997 for a new Securities and Investment Board (SIB) with statutory powers, this has not reduced the value of this discussion paper which raises some wider issues on methods of regulation.

The paper excludes the supervision and regulation of banks, building societies, insurance companies and exchanges and concentrates on areas that directly affect the public on an ongoing basis. It looks at the expectations of the main parties involved in regulation, the theory and practice of regulation, opportunities and concerns, and concludes with a summary of key issues for discussion. The thrust of the paper is that self regulation should be replaced by statutory regulation and that the present ‘prescriptive’ regulatory process should be replaced by one based on ‘outcomes’ supported by guidance.

The provision of graduated mortality rates, for the United Kingdom pensioners' experience, based on the so-called ‘amounts’ data sets is addressed. Specifically a methodology is investigated, building on the existing methods practiced by the CMI Bureau, which takes a more detailed account of the underlying structure of the data involved. The method is applied to the U.K. pensioners' experience and recent mortality trends in this experience revealed.

The present paper is in two main parts: (1) a general discussion of the population factors which have led to a focusing of attention upon ageing with some reference to recent advances in gerontology and (2) a consideration of the actuarial implications of current gerontological research.

In November 1983 I gave a talk to the General Applications Section of the Royal Statistical Society jointly with the Institute of Actuaries Students' Society, entitled “Time-Series Analysis in Investment Models: Inflation and Share Prices”, in which I outlined the statistical derivation of a stochastic investment model. This model was presented to the actuarial profession in a paper “A Stochastic Investment Model for Actuarial Use” discussed at the Faculty of Actuaries in November 1984. The statistical background, and other information, is discussed in Occasional Actuarial Research Discussion Paper No. 36, “Steps Towards a Stochastic Investment Model”, which is a sort of Appendix to the Faculty paper. It contains most of the material presented to the Students' Society in 1983.

The Faculty paper described a number of possible applications of stochastic investment models. I stated there that a “stochastic model for investments … can be used by actuaries in almost any circumstance where a rate of interest enters their calculations at present”. That is a pretty wide field. But I suggested that it opened up “wider possibilities for investigation too”. I intend in this paper to describe a number of simple applications of my stochastic investment model, in order to show the flavour of how such a model can be used. None of the topics has been comprehensively investigated, and I am sure that the reader will soon ask questions which I have not answered. I hope that he will be able to think of ways of answering them himself.

This paper extends the theory of graduation by parametric formulae to include dynamic estimation methods. This is an application of the Kalman filter and allows the parameters of the curve fitted to vary with age. The amount of variation is determined by the amount of smoothing required, and the method can be regarded as a combination of curve fitting and sequential smoothing, each of which has been used separately for performing graduations. In practice, a dynamic straight line can always be used for the graduation and the method has a sensible logical interpretation.

The discovery of some general Law of Mortality, by means of which the values of the contingencies, depending upon human life, might be expressed in some simple formulæ, without the necessity of performing the numerous calculations which are required even for the chances of a single life, and still more in the various eases, in which two or more lives are involved, has occupied the attention and labours of many scientific men. But the result has not hitherto been satisfactory, in spite of the skill with which their investigations have been conducted, and the unwearied patience which they have brought to the task. The failure has probably arisen from the want of a sufficient number of observations, the authenticity of which could be relied upon; or for want of that accuracy in the data, without which it is in vain to attempt to find the traces of a regular law, disturbed as it must be by the peculiar circumstances under which the observations were made, or by the ignorance, and, in some cases it may be, by the wilful errors of those who have been employed to collect the facts.

This discussion meeting was on the subject of business ethics, with particular reference to the work of actuaries.

As an introduction to the meeting, copies of the paper, ‘Business Ethics: the New Bottom Line’, by Sheena Carmichael, were distributed to members of the Institute.

Sheena Carmichael is the director of ETHOS, a consultancy dedicated to helping organisations identify and manage ethical issues. She is a research associate at the European Institute of Business Ethics at Nigenrode University in the Netherlands.

The paper ‘Business Ethics: the New Bottom Line’, was published in 1995 by Demos, which “is an independent think-tank committed to radical thinking on the long-term problems facing the United Kingdom and other advanced industrial societies.

It aims to develop the ideas — both theoretical and practical — that will shape the politics of the 21st century, and to improve the breadth and quality of political debate.” It is a registered charity.

The paper has not been reproduced in British Actuarial Journal, but further information can be obtained from:

Demos, 9 Bridewell Place, London, EC4V 6AP; telephone: 0171 353 4479; facsimile, 0171 353 4481; email, [email protected]

It is commonplace to remark that probability lies at the root of actuarial science. It is equally commonplace that there has been—and still is—considerable dispute over the definition of probability and that such dispute is usually of little consequence in practical calculations. This being so, some may wonder why I have chosen to ventilate once again the philosophical problems which encompass the concept of probability and which commonly bedevil discussions of what is meant by propositions of the form ‘The probability of x is y’ or ‘A is more probable than B’. The solutions which may be offered to this type of problem are not likely to affect the amount of a surrender value or the contribution scale of a pension scheme. On occasion they may affect the answers to estimation problems or decisions based upon significance tests, although even here the differences between the results yielded by alternative methods of approach are commonly negligible.

The subject of Life Assurance Investments does not seem to have been discussed for a long time at the meetings of the Institute. Two valuable and instructive papers, bearing the honoured names of Mr. Samuel Brown and Mr. Arthur H. Bailey, were read to the Institute respectively on 25 January 1858 (J.I.A., vii, 241) and 24 February 1862 (J.I.A., x, 142), but they appear to be the only contributions of importance, dealing with the question in its entirety, to be found in the Journal. Notwithstanding the lapse of time which has taken place since the latter date, the principles of investment as defined by these two distinguished authorities are still very generally applicable to present needs; and the articles themselves have lost none of their charm for the student of life assurance finance, characterized as they are by soundness of judgment and by felicity of expression.