These notes discuss the Proposal by the Commission of the European Communities for a Council Directive “On the implementation of the principle of equal treatment for men and women in occupational social security schemes”. Article 6, sections l(h) and (i) of the proposed Directive state that it would be contrary to the principle of equal treatment to provide for benefits whose level or amount differ or to set contributions at different rates, “by taking into account different factors of calculation, actuarial or otherwise, with regard to the phenomena of ill health, mortality or life expectancy”. These notes concentrate on this proposal, which is of considerable actuarial importance. Actuaries take into account different factors of calculation with regard to these phenomena, not simply by convention or through unjustifiable prejudice, but because of a sincere respect for the truth. To attempt to ignore the truth may have dangerous consequences, which are discussed.

Mr. President, Sir, when I received the invitation to give this lecture I felt greatly honoured. I accepted for two reasons. First, for a Fellow of the Institute of Actuaries such an invitation from the Faculty is in the nature of a Royal Command. Secondly, the suggested subject is a natural extension of the field in which I have specialised so far in my professional life.

1.1. The European Economic Community forms the world's largest trading block of countries, accounting for approximately one-third of world trade. Legally it consists of:

• —The European Coal and Steel Community (ECSC); formed 1951.

• —The European Economic Community (EEC); established by the Treaty of Rome in 1957; and

• —The European Atomic Energy Community (EURATOM); established by separate treaty at the same time as the EEC.

1.1.1. In October 1980 the Council of the Faculty of Actuaries set up a Working Party with the following brief:—

• (1) To investigate the criteria by which the solvency of life assurance companies should be assessed and to determine the amount of the solvency margin which should be required in practice by supervisory authorities. The existing requirements of the E.E.C. Life Establishment Directive should be considered with a view to recommending any desirable alterations thereto to be made when those requirements are reviewed in due course by the E.E.C. Commission. In carrying out its work the Working Party should co-operate with Working Parties or Committees of other actuarial bodies.

• (2) To report the result of their investigations to Council.

1.1. The purpose of this paper is to present to the actuarial profession a stochastic investment model which can be used for simulations of “possible futures” extending for many years ahead. The ideas were first developed for the Maturity Guarantees Working Party (MGWP) whose report was published in 1980. The ideas were further developed in my own paper “Indexing Long Term Financial Contracts” (1981). However, these two papers restricted themselves to a consideration of ordinary shares and of inflation respectively, whereas in this paper I shall present what seems to me to be the minimum model that might be used to describe the total investments of a life office or pension fund.

1.1. All speculative activities seem to breed deeply-held but unsupported beliefs. Some of these, for example in horse-racing, might be expected to relate to natural laws and be susceptible to analysis, which they do not normally receive. Others, such as any so-called system for winning at roulette, can be dismissed without observation.

1.1. These guidelines apply to the bases of calculation of individual transfer values from retirement benefit schemes and to the assessment of benefits in such schemes in respect of incoming transfer payments.

1.2. The guidelines apply whether the actuary is acting as an individual, as a partner, as a director of a corporate body or in the course of his employment.