This subject, as it left the hands of Simpson, Halley, Dodson, &c., is fully discussed in the appendices of Francis Baily's work on interest and annuities. These, with Milne's note on the subject (vol. ii., p. 680), Jones's notice of the problem, and the various modes of approximation announced in the pages of this Journal, give all I have found written about the matter in modern times. Referring to the citations in Baily for the history of the question subsequent to 1680, I give what I have found in previous time; and I add a few new formulæ for consideration. The problem is, I doubt not, of infrequent occurrence. It never occurred to myself to want more than a look at the tables would furnish; but it may be suspected that, as the requirements of business become closer, inverse problems will acquire more importance than they now possess.

Expert judgement has been used since the actuarial profession was founded. In the past, there has often been a lack of transparency regarding the use of expert judgement, even though those judgements could have a very significant impact on the outputs of calculations and the decisions made by organisations. The lack of transparency has a number of dimensions, including the nature of the underlying judgements, as well as the process used to derive those judgements. This paper aims to provide a practical framework regarding expert judgement processes, and how those processes may be validated. It includes a worked example illustrating how the process could be used for setting a particular assumption. It concludes with some suggested tools for use within expert judgement. Although primarily focussed on the insurance sector, the proposed process framework could be applied more widely without the need for significant changes.

The authors have reviewed over 60 texts on the subject of Enterprise Risk Management (ERM). In this paper they set out a summary of ERM based on three of those sources, selected for their relevance and breadth of view. The paper observes that the approaches described vary widely in nature. A separate ‘on-line” source is provided, which summarises key readings from the 60 texts. Combining findings from these texts with the authors' own experiences, the paper suggests some best practice checklists, designed to enable organisations to take stock of their current ERM frameworks. It discusses other aspects of ERM for practitioners, including extreme events, opportunity management and the link with corporate strategy. The paper looks at immediate and longer-term implications for actuaries in the United Kingdom, and then poses questions about future professional development and education. It suggests an emerging role for the ‘ERM actuary’, and, finally, it suggests future work to progress the development of ERM and the actuaries' role.

This paper was written at the request of the Life Research Committee of the United Kingdom Actuarial Profession's Life Board. It concerns the valuation of U.K. with-profits business, with particular attention to the market-consistent ‘realistic reporting’ basis currently being used in the U.K. by the regulator, the Financial Services Authority (FSA). The paper surveys recent regulatory activity concerning the development and introduction of the new valuation approach, and puts it into the context of a survey of alternative methodologies, both deterministic and stochastic. The particular issues arising when considering prudential solvency are discussed, and various approaches are reviewed and compared with market consistent methods. Numerical examples are given, which demonstrate potential issues (regarding comparability and consistency) with the FSA's proposed approach — in particular the sensitivity of results to model calibration. The authors support the FSA's move to a stochastically-based framework for solvency measurement, but highlight some issues which need to be taken into account.

In recent years an unusually high proportion of the papers submitted to the Institute and to the Faculty have dealt with technical problems of life assurance management. The subjects covered include investment policy, valuation and bonus policy, the relationship between liabilities and assets and the relative merits of with-profit and without-profit business. The object of this paper is to indicate how these various subjects (with the addition of new-business policy) react on each other and to consider how far any over-all actuarial planning is possible, special regard being paid to modern developments in the different fields. Some repetition of what has already been said in recent years is inevitable, but no attempt will be made to summarize actuarial opinion on the topics under review, a task which would be impossible within the scope of the paper.

The actuary's expertise in the field of life insurance lies mainly in the application of mathematical and statistical techniques to the wide range of issues associated with life insurance business. In particular, the actuary has developed very sophisticated tools for modelling and forecasting and to help in establishing equity between policyholders. In recent years, owners of such businesses, be they policyholders or shareholders, have been coming to depend increasingly upon the actuary's skills to establish value for their overall business. On an ongoing basis, these requirements relate to such things as the need for more complete balance sheet presentation in the case of a proprietary company. Additionally, and inevitably, the actuary is drawn into the world of financial dealing in respect of takeovers and mergers where he is becoming exposed to the commercial risks inherent in being an ‘expert’. The stakes are increasing and in the larger cases hundreds and even thousands of millions of pounds are involved. In this world, the actuary can expect to be subject to a range of pressures from clients, media, takeover rules and so on, all of which are well removed from the actuary's traditional comfort zone. As the stakes increase, so does the threat of litigation.

The authors have recently been involved, one as principal and one as actuarial adviser, in the largest hostile takeover in the life insurance industry in the U.K. and, in the process, many issues of significance to the individual and the profession as a whole were exposed. This paper is intended to address this very important area and to flag some areas which could prove to be of increasing concern to the individual and to point to some where the Institute may wish to become involved.

The aim of this paper is to examine and document a scientific approach to establishing an estimate of the economic value or range of possible economic values of a life assurance enterprise.

This is essentially a practical paper which provides a ‘practitioner's guide’ to performing an actuarial appraisal of a life assurance company rather than providing a rigorous theoretical derivation of the methods. There is, however, a philosophical issue, that of an appropriate risk rate of return, which cannot be completely side-stepped in a paper on appraisal values. This issue is briefly covered in Section 3. It should be noted, however, that an entire paper could be devoted to this subject.

The paper finishes on a potentially controversial note, that of UK Generally Accepted Accounting Principles (UK GAAP) for life assurance companies, suggesting that the appraisal value techniques outlined in this paper could play a major part in formulating UK GAAP.

Is there a mathematical formula which will express the way in which mortality changes age by age? Many students have sought that will-o'-the-wisp but have had to confess failure. For example, Sir William Elderton says:

This paper shows how the powerful and flexible tool of stochastic modelling can be applied to a range of business decisions extending far beyond the asset allocation solutions that are common to many asset/liability modelling studies. The example used to demonstrate these techniques is a general insurance case study, but similar principles can be extended to many different business situations. At each stage of the analysis we consider the implications of modern financial theory on the management decision process together with a practical perspective on observed behaviour in the real world. Opportunities are taken to suggest directions in which further research may be of benefit to the actuarial profession.

The combination of increasing vulnerability and intensity of natural disasters has led to severe humanitarian impacts in recent years. The uncertainty of environmental change and growing populations suggests that this trend is a cause for significant concern. Increasingly, nations are seeking additional methods to increase their financial resilience to disaster events. Sovereign disaster risk financing and insurance (SDRFI) may be the panacea for managing disaster risk at a national level. However, there is a need for better evidence to enhance, guide and support these programmes. The design of SDRFI programmes aim to maximise their impact and reduce the human and economic cost of disasters. This paper presents an overview of 16 technical background papers that offer insights into the development of an impact appraisal methodology for SDRFI evaluation. The papers are part of a joint project between the UK Department for International Development and the World Bank and the Global Facility for Disaster Reduction and Recovery.

This paper considers the approaches currently used by life offices for statutory valuations, and proposes a number of changes to current practice. It builds on the earlier work of Philip Scott's Working Party and a working party which reported on all aspects of unitised with-profits business to the 1996 CILA conference.

Recommendations are made for each of the major categories of long-term business, in particular for the introduction of a bonus reserve standard for accumulating with-profits business, whilst retaining the net premium standard for conventional with-profits business. It is proposed that the current net premium approach for non-profit business should be replaced by a gross premium method. The paper also develops a greater codification of the calculation of non-unit reserves on linked business.

Considerable emphasis is placed on the requirement for statutory reserves to have regard to PRE. It is assumed throughout that the E.C. Third Life Directive remains in its current form.

A number of examples are provided which illustrate the proposed method for accumulating with-profits business. Appendices to the paper include a draft of suggested consequential changes to the Insurance Companies Regulations 1994, and a revised supporting version of the whole of GN8.

It is, indeed, an honour and pleasure to write a guest editorial for British Actuarial Journal. The guidelines stated that my topic could be ‘education’, so, as a lifelong educator (whether any students became educated is another matter), I have chosen that topic as my focus.

In this paper, we examine the hedging performance of the new FTSE 100 Share Index. First, we reconstruct a back-history of the monthly and daily index values using the London Share Price Database. Then we analyse the statistical characteristics of the Index, comparing it with the FT–Actuaries All Share and FT Ordinary Indexes. Finally, we examine the sources of undiversification within the FTSE Index. We conclude that the market is likely to track the FTSE Index to within a close tolerance, and that the residual tracking error is attributable partly to sector imbalances, but more importantly, to imbalances in exposure to smaller capitalization stocks.

More than 200 years ago, on 30 April 1760, Daniel Bernoulli (1766) read a memoir to the Royal Academy of Sciences in Paris entitled Essai d'une nouvelle analyse de la mortalité causée par la petite vérole, et des avantages de l'inoculation pour la prévenir (see Bradley, 1971, for a translation). In this remarkable memoir Bernoulli produced the first double decrement life table and one of the related single decrement tables, as well as deriving a mathematical model of the behaviour of smallpox in a community. This model was the forerunner of considerable developments in the mathematical theory of infectious diseases, a description of which is given in N. T. J. Bailey (1975). During the half century following Bernoulli's memoir there were a number of papers by other authors on the subject of that memoir; these, and the original memoir, seem to be little known to actuaries and are the subject of the present paper. They could have been the starting point of the actuarial development of exposed-to-risk formulae, but in fact were not.

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.

Our earlier paper ‘The money supply, economic management and the gilt-edged market’ (J.I.A.96, 1) introduced the money supply as being ‘of importance to investment, in general because of possible changes in the economic management in the United Kingdom, and in particular because of the possible implications for the gilt-edged market’. To a large extent these changes have come about; the Authorities are now placing greater emphasis than in 1969 on controlling the money supply and support for the gilt-edged market was withdrawn when the Bank of England published Competition and Credit Control in May 1971.

2. The present paper is more fundamental for investment. The introduction to the earlier paper referred to our main research project into the uses of the financial statistics which were first published in 1962 as a result of the Radcliffe Committee Report. Changes in the management of the economy and the gilt-edged market were side issues, however important; the present paper describes some of the interim conclusions of the main project which is still continuing.