Older people are higher contributors to mortality excess and most sensitive to environmental influences, e.g. temperature. As the population ages, variability in temperature is liable to impact a large proportion of life insurance or pension policies in a portfolio. Climate change is projected to significantly affect future mean temperatures. Moreover, future changes in mean temperature are estimated to vary across different regions of the United Kingdom. Accordingly, the present paper investigates the potential impact of future mean temperature changes on older-age mortality in England & Wales and Scotland. The corresponding effect on older-age mortality differences between England & Wales and Scotland is also investigated.

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.

1.1 A number of papers have been written in recent years that discuss the valuation of the business of a life office, examples of these are Burrows and Whitehead (1987) and Bunch (1986). These papers recognize the need to use a risk adjusted discount rate in the calculations. Burrows and Whitehead devote a section of their paper to the determination of such a rate. In their abstract they state that “…an entire paper could be devoted to this subject”. This latter point is supported by the existence already of a number of papers in the finance literature on the very topic of determining risk adjusted discount rates e.g. Robichek and Myers (1966), Fama (1977).

1.2 This paper outlines some results of the theory of determining risk adjusted discount rates and the valuation of risky cash flows as developed in the finance literature, and discusses the application of this theory to the determination of life office appraisal values. Some comments are made on Section 3 of the Burrows and Whitehead paper.

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.

It is the object of the present article to put together a number of formulae which it may be useful to the actuary to find in one place. At the same time it may show all persons who possess an elementary knowledge of algebra, that they may, with no great amount of tables, and processes of very easy application, learn to compute the value of any benefit in which the duration of one life only is concerned. The same principles, with more extensive tables, apply to cases in which two or more lives are involved.

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.

1. Capital is wealth appropriated to reproductive employment, and, in the words of the late J. S. Mill, “the gross profit on capital may be distinguished into three parts, which are respectively the remuneration for risk, for trouble, and for the capital itself, and may be called insurance, wages of superintendence, and interest.”

It is with the last of these, Interest, that we have at present to do.

2. In civilized communities wealth is measured in money, and therefore in our investigations it is of money that we shall speak; but evidently it is immaterial, in laying down general propositions, whether the standard units are of one actual value or of another, so long as we remain consistent with ourselves, and use the same standard throughout. We shall therefore, as the most convenient course to suit all currencies, treat of units of value, without specifying to what currency these units belong.

The earliest event of the year 1844 was the presentation to Parliament of the “First Report” of the Committee on Joint-Stock Companies, appointed in 1841. The report set out by stating that, as a good deal of the information affecting persons was in the nature of ex parte statements, caution would be required in promulgating it: hence much of the evidence collected would he stated summarily. I shall confine myself here to the passages bearing upon Insurance Associations.

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.

Some years ago I had the privilege of reading a paper on Contingent Reversions, &c., before this Institute, and the proposals I then made for the treatment of the premiums on the insurances to be set up in connection with reversionary transactions were received with general condemnation, nor have they since, so far as I know, met with any practical support, although I have seen no reason to alter my opinion of the soundness and practicability of the views I then put forward. I am not afraid on this occasion of meeting with like opposition, as the methods I am now going to deal with have been carried into practice already by the Society with which I am connected, and by way of reassurance, if not otherwise, have examples on the books of many of the life offices, both in England and Scotland.

In a paper by the late Mr. Samuel Brown “On the Rate of Mortality and Marriage among Europeans in India” (J.I.A., xi, 1), reference is made to a method used by Griffith Davies to deduce rates of mortality from the records of the Madras Military Fund. It appears that Davies ascertained the average age of the lives in each of certain groups into which the experience naturally divided itself, and obtained the ratios which the actual deaths in the several groups bore to the corresponding number expected according to the Northampton Table at the average age. These ratios were then set out as ordinates corresponding to abscissae representing years of age, and a continuous curve was drawn in the usual way, by reading off which the graduated ratios for each age were obtained, and from these the graduated rates of mortality were at once formed.