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.

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.

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.

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.

1.1 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.

The prediction of outstanding claims amounts in non-life insurance is, by its very nature, highly speculative. Partially because of this and partially because of the variety of features suggested by various researchers for possible inclusion in the structure of the underlying prediction model, the past two decades have seen a proliferation of methodologies for making such predictions. Specific details of these developments are contained in a comprehensive and highly detailed survey conducted by Taylor (1986) in which a taxonomy of methods is established. One feature common to all of these methods is the utilization of current and past records of claims amounts—invariably in the form of the familiar so-called runoff triangle or a variant thereof—to calibrate the proposed prediction model before use. Prudence dictates that diagnostic checks should then be made to establish whether or not the data are supportive of the structure imparted to the prediction model before use, a feature which apart from some notable exceptions including Zehnwirth (1985) and Taylor (1983), is not always emphasized in the literature.

In a recent paper, Kremer (1982) has shown how the classical chain ladder method for estimating outstanding claims on general insurance business is strongly related to a two-way analysis of variance. It can be argued that the estimation methods in a standard chain ladder analysis are inefficient from a statistical viewpoint and that an analysis of variance is more appropriate. Once the chain ladder method is identified with a standard statistical method, the well-known statistical theory can be used to the advantage of the claims reserver. For a further discussion of the use of main stream statistical theory applied to the least squares estimation of the linear model which is close to the chain ladder method, the reader is referred to Renshaw (1989).

1.1 The traditional approach in the United Kingdom to the analysis of permanent health insurance (PHI) data and to the rating of PHI business has been the Manchester Unity approach. This approach, which has its origins in Friendly Society business, is in some ways unsuitable for modern PHI business. (An interesting discussion on this subject can be found in Report No. 7 of the Continuous Mortality Investigation Bureau (C.M.I.R. 7, §4 (1984). For this reason the PHI Sub-Committee of the CMIB has recently been investigating the possibility of using a different approach, involving the use of a multiple state model, for analysing PHI data. A full report on the Sub-Committee's investigation will be published soon as C.M.I.R. 10.

The following paper sets out the actuarial basis for the Cologne Re model projecting the spread of AIDS. We project new infections, new AIDS cases, and deaths for the sexually active population and demonstrate the effect on the German life assurance industry.

1.1 The traditional approach to examining the financial status of a company is to look at the balance sheet and the profit and loss account. Such information is usually publicly available, it is certified by the auditors as having been drawn up according to relevant accounting standards and it is generally presumed to communicate reliable information.

1.2 In the case of a manufacturing or trading company the profit and loss account records purchases and sales and the balance sheet will include a valuation of stock in hand, since it is anticipated that this will give rise to future sales income. Working capital is required because products have to be manufactured or purchased before they can be sold. Profit is realized when the product is sold for more than it cost to buy it or to make it.

The computer language APL is not as well known in the financial field as it might be and yet its structure and syntax make it very well suited to financial and actuarial calculations (as well as to mathematical and statistical calculations)—indeed it might almost be called a natural language for financial calculations.

In a contribution to the XVI ASTIN Colloquium in Liège, 1982, entitled ‘Description and Comparison of various Programming Languages and their Suitability for Non-Life Actuaries’, J. A. Bartola concluded that APL was a very attractive programming language for actuaries.

This paper describes the Corporate Planning system which has been developed in my office over the last 6 years or more. It first makes a high level pass through the various components and how they fit together and then looks in more detail at some of the components.

1.1 In this paper I intend to concentrate on the application of mathematics and the problems faced and (sometimes) solved by such application, rather than on the mathematics itself. That is not to belittle the mathematics in any way, and I would like to acknowledge at the start that the stochastic financial model which underlies the results given in this talk is based on Professor Wilkie's model as detailed in T.F.A.39, 341.

In an earlier paper the control characteristics of the aggregate method of funding were displayed by way of its response to a spike, step and random variation in the earned rate of interest, together with a simple intuitive method of setting the valuation rate of interest.

The projected unit method is analysed here in the same way.

A further algorithm is developed which aims at driving an opening fund and contribution rate to a desired fund and contribution rate in n years, using the smoothest path of contribution rates.