In this paper, a long-term equilibrium model of a local market is developed. Subject to minor qualifications, the model is arbitrage-free. The variables modelled are the prices of risk-free zero-coupon bonds – both index-linked and conventional – and of equities, as well as the inflation rate. The model is developed in discrete (nominally annual) time, but allowance is made for processes in continuous time subject to continuous rebalancing. It is based on a model of the market portfolio comprising all the above-mentioned asset categories. The risk-free asset is taken to be the one-year index-linked bond. It is assumed that, conditionally upon information at the beginning of a year, market participants have homogeneous expectations with regard to the forthcoming year and make their decisions in mean-variance space. For the purposes of illustration, a descriptive version of the model is developed with reference to UK data. The parameters produced by that process may be used to inform the determination of those required for the use of the model as a predictive model. Illustrative results of simulations of the model are given.

A FIMAG Working Party was set up in 1989 to consider the stochastic investment model proposed by A. D. Wilkie, which had been used by a number of actuaries for various purposes, but had not itself been discussed at the Institute. This is the Report of that Working Party. First, the Wilkie model is described. Then the model is reviewed, and alternative types of model are discussed. Possible applications of the model are considered, and the important question of ‘actuarial judgement’ is introduced. Finally the Report looks at possible future developments. In appendices, Clarkson describes a specific alternative model for inflation, and Wilkie describes some experiments with ARCH models. In further appendices possible applications of stochastic investment models to pension funds, to life assurance and to investment management are discussed.