Papers and reports

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. 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. Insurance work in the United Kingdom uses the notion of reserves for mismatching.

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 TFA, 39.

In a recent paper, Kremer 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.

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.

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 in which a taxonomy of methods is established.

The first stage of the work of the Working Party was to gather information on current actuarial involvement in life assurance supervision and control, statutory and non-statutory, in the 12 countries of the European Community (‘the EC’). The results of this research are given in the Appendix. The paper draws on this research and aims to set the scene for a debate on the future involvement of the actuarial profession in a ‘harmonized’ European life assurance industry.

This paper considers the valuation for solvency purposes of traditional long-term insurance business. It concentrates on without-profits 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.