The paper describes the philosophy of with-profits business which has been developed in the authors' office, as a practical illustration of the running of such business in modern conditions. A description is given of how the philosophy is implemented in the main areas of actuarial management, including valuation methods, bonus distribution, product design and expense control. The discussion is extended to address a number of topics which are the subject of current debate including the financial strength of offices, future bonus prospects and disclosure of expenses.

1.1 The Working Party on AIDS was established in April 1987 to give the profession information about, and to take any necessary action in relation to, the problems posed by HIV infection and AIDS. Three Bulletins have been issued by the Working Party, in September 1987, December 1987 and July 1988 (Institute of Actuaries Working Party on AIDS, 1987, 1987a and 1988a). These Bulletins covered what the Working Party saw as the important aspects of the problem from the point of view of the profession. They outlined what was then known about the epidemiology of AIDS, made some provisional projections as to its possible impact, and the sensitivity of such projections to the assumptions used, examined the implications of the underwriting process in relation to AIDS, and pointed out where action seemed to be required in relation to underwriting, premium rating, product design and reserving.

This paper is the report of a Research Group which has been examining developments in calculating devices, the effects on actuarial work and the future outlook.

The paper considers the valuation for solvency purposes of traditional long-term insurance business. It concentrates on without-profit business, and discusses the reserves that are required to protect against the contingency of sudden adverse changes in asset values (the ‘mismatching’ or ‘resilience’ test). The details of a suitable test, and a method of applying it in practice using a ‘matching rectangle’, are described. Investigations into the effectiveness of such a test, using both deterministic and stochastic methods, are followed by concluding remarks on the underlying philosophical issues raised.

Full numerical results are presented in the Appendices.

The purpose of this brief note is to comment on the methodology used by Benjamin and Michaelson in their estimation of the expectations of life for non-smokers and smokers and the differences between these expectations of life.

The author of this note has discussed the methodology with the first author of this earlier paper and with their research assistant.

1.1 1992 has become a symbol. A symbol of change in a Europe which feels itself threatened by the economic might of America in the West and Japan in the East. 1992 really does mean that millions of people, despite wide gulfs of language and culture, and a history of often bloody conflict between them, are making one more effort of collective will to club together in the belief that the one thing they have in common, geography, is sufficient reason to disguise differences and create a powerful economic union for the greater benefit of European suppliers and consumers.

1.1 A paper about the Appointed Actuary is essentially a paper about prudential supervision of life insurance companies. The system which has operated in the UK since the mid-1970's is only partly one of Government supervision. Through the professional role of the Appointed Actuary, it also contains elements of a system of self-regulation with the Institute and Faculty of Actuaries standing in place of SRO's. Unlike the self-regulatory arrangements of the Financial Services Act, though, this second part of the system has grown up by custom and practice and in certain respects it is not codified. However it enables the Insurance Companies Act to be operated successfully.

The two approaches to modelling aggregate claims—the individual and the collective models—have been regarded as arising by considering a portfolio of policies in different ways. The individual risk model (IRM) is derived by considering the claims on individual policies and summing over all policies in the portfolio, while the collective risk model (CRM) is derived from the portfolio as a whole. This is sometimes held to be the main difference between the IRM and the CRM. In fact the IRM can be derived in exactly the same way as the CRM and can be regarded as a compound binomial distribution. This makes a unified treatment of risk models possible, simplifies the calculation of the mean and variance of the IRM, and facilitates the calculation of higher moments.

The distribution of insurance claims in a given time period is usually regarded as a random sum. This paper sets up a time series model for the value of the claims and combines it with a model for the number of claims. Thus past observations can be used to make predictions of future values of the random sum, and the overall model ensures that they are discounted appropriately. It is shown that explanatory variables can be introduced into the model, and how it can be extended to handle several groups. The general approach is based on the recently developed structural time series methodology.

1. In a recent article in this Journal, Professor Wilkie gave an account of the determination of the rate of interest in a Fisher–Hirshleifer model. In his analysis of a production economy (§§3–7), he appeared to take as intuitively reasonable, not to say axiomatic, the existence of an inverse monotonic relation between the value of investment and the rate of interest. ‘A reduction in the auctioneer's rate of interest will stimulate capital investment.’ (p. 290) Now one of the conclusions to emerge from the capital theory debates in economics of the 1950s and 1960s is that the value of investment is not in general an inversely monotonic function of the rate of interest (see, for example, Harcourt). The purpose of these Notes is to alert actuaries to the existence of this conclusion and discuss some of its implications. To achieve the first objective, I shall need to construct a simple model—this is done in §2. I devote §3 to the analysis of the relation between the value of investment and the rate of interest. I discuss wider implications and draw some conclusions in §4.

1.1 The basic task of actuarial valuation is to compare the quantity of assets with the quantity of liabilities. A refinement is to compare qualities as well as quantities.

1.2 The qualities of assets and liabilities are their characteristics of cash flow, duration, growth, price volatility, etc. This note considers a conceptual and mathematical framework for matching in the most general terms.

1.3 Insurance work in the United Kingdom uses the notion of reserves for mismatching. Pension fund valuations in the U.K. also tend to use a notion of matching when considering the actuarial value placed on the fund.

The paper discusses two important models of option pricing: the binomial model and the Black—Scholes model. It begins with a brief description of options.