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.