1.1. For a number of years now it has been a commonplace amongst actuaries actively involved in unit-linked business that it was time someone wrote a paper dealing adequately with the subject of unit pricing. To those not actively involved with the subject the absence of such a paper may seem unimportant, but the fact is that the price-making process is central to the whole conduct of linked life business. It exerts a major influence upon the profitability and solvency of the office, and upon the relative interests of different classes and generations of policyholders and shareholders. In this respect, it is analogous to the bonus policy of a with profits office.

1.1 On 21 December 1976 I received the following memorandum from Mr A. E. Tinckler, who was then the Actuary of my Company. It read:

1.2. “We have been discussing recently some of the effects on the Life Fund of a significant fall in interest rates, and I think we agree that the time has now come to set up a formal study to analyse the problem and to make recommendations.

1.3. “There is no doubt that interest rates in the United Kingdom are very much higher at the present time than in other comparable countries. There are good reasons for this state of affairs, but it is most unlikely to continue over more than a few years, unless the country is to descend to very low levels indeed in the international league. In spite of many pessimistic assertions to the contrary, there are good grounds for thinking that the present rates will come down very substantially indeed over the next few years.

1. In the following experiments I simplify enormously, by assuming that the only benefit provided is a pension on retirement at age 65, that there are no benefits at all on death, not even a return of contributions, and that there are no ill-health retirements or early retirements. I also assume that all salaries, contributions and retirement pensions are paid annually in advance. This simplifies the calculations and hardly affects the results. I also assume complete certainty of inflation. salary increases and investment returns. The purpose of the experiment is to investigate the relationship between the amount of pension that may be deemed to have ‘accrued’ each year, and the amount of contribution (as a percentage of salary) needed to purchase the extra pension that has accrued in each year. under both a final salary defined benefit scheme and a revalued average salary scheme.

1. The Universal or Variable Linked Life Assurance policy has been issued by a number of companies in the United States of America and in the United Kingdom, and it is now reasonably familiar in the marketplace. It does not appear to have received much attention in actuarial literature, perhaps because of its simplicity, though a paper has been presented to the Institute of Actuaries Students' Society (Sheraton, 1984). So far as I know the corresponding Variable Linked Life Annuity has not been issued by any office, and some of its features are slightly different from those of the Life Assurance policy.

1. This note was inspired by the paper ‘The Matching of Assets to Liabilities’ presented by A. J. Wise to the Institute in March 1984 (Wise. 1984b). In it he presented a method of looking at the problem of matching which I claimed in the discussion was essentially a portfolio selection approach. However, his approach had a number of novel features. I wish to discuss one of these, approaching it from the conventional portfolio selection viewpoint. I am not aware that this problem has been considered elsewhere in the substantial literature that exists on portfolio selection. Full discussion of the mathematics of the conventional portfolio selection problem is contained in Sharpe (1970) and Szegö (1980), and a general explanation is available in many modern financial text books, and in the Institute paper by Moore (1972).

Edmond Halley, who was born in 1656 and died in 1742, is well known generally because of the Comet which bears his name. He is not, however, associated to any great extent with other activities and if it were not for the Comet it is likely that most people today would never even have heard of him. Outside the actuarial profession, and perhaps to some extent even within it, it is not generally known that in 1693 he constructed a life table from the bills of mortality in the German city of Breslau and then went on to calculate from that table annuity rates on one, two and three lives. Reference to this was formerly included in the introduction to the Year Book, but this has now been shortened and the reference to Halley has disappeared.