The purpose of this paper is to discuss the actuarial principles on which the investment policy of life assurance offices should be founded. The policy considered relates, firstly, to the principles on which the selection of investments should be made and secondly, to the basis of their subsequent valuation.

The paper traces the history of the development of a with-profit system for a specialist unit-linked office. The marketing problem, to which this was the chosen solution, is discussed and a number of possible future developments are then considered. The second half of the paper is devoted to discussion of the question of matching assets and liabilities for the range of products developed. Although the paper deals with developments in a particular office the authors' intention is to provide a different perspective on the problems associated with conventional with-profit business which will be of more general interest.

A Dread Disease contract pays out a lump sum on the diagnosis of any of a number of specified diseases. Those most commonly covered are heart attack, coronary artery disease requiring surgery, cancer and stroke. The benefit can take either of two main forms—it may provide an acceleration of all or part of any death benefit or it may be an additional benefit. It can be sold in conjunction with many conventional products or as a stand-alone policy.

Dread Disease contracts were originally developed in South Africa in the early 1980's, although cancer riders had previously been sold in the U.S.A., Japan and Israel. To some extent the marketing of these contracts was insensitive and preyed on people's fears in a distasteful way. This may explain some initial reluctance amongst U.K. insurers to enter this market; however with marketing literature now emphasizing more positive aspects, this appears to have been overcome.

Some combinations of ideas seem strange and unfamiliar. Life assurances with participation in profits—what could be more natural? But annuities with participation in profits?—the association of such discrepant ideas gives rise to all manner of objections in our minds.

The paper is largely concerned with discussing what is a suitable valuation basis for deciding the rate of bonus an office should declare if it wishes to maintain this rate of bonus in the future as long as conditions remain reasonably stable.

Because of recent developments, such as the substantial proportion of the assets now held in ordinary shares, the reverse yield gap, the present historically high rate of interest and the growth of immediate annuity and other single premium business, a net premium valuation in conjunction with assets at balance sheet values gives an inadequate view of the position of an office. With the advent of electronic computers a more realistic and comprehensive view is now possible, and the paper advocates a valuation of the liabilities on a modified bonus reserve basis with rates of interest and bonus the same as those implicit in the current premium rates, and a valuation of the assets at a notional rate of interest equal to the rate used in the valuation of the liabilities. The various problems arising in the valuation of assets, and especially of ordinary shares, at a notional rate of interest are discussed, and also the adjustments necessary if the assets and liabilities are not fully matched.

The final decision on the rate of bonus to be declared must in the end be a matter of judgment, as it depends on many factors which cannot be accurately forecast, such as the future course of the rate of interest, the amount of new business and the rates of premium charged. Nevertheless, it is now possible to make this decision in the light of a very much fuller analysis of the position than has probably been made in the past.

Using the stochastic investment model proposed by Wilkie (1995) this paper simulates the progress of a specimen final salary pension scheme over a period of 25 years. Salary experience over the projection period is also assumed to be stochastic. The specimen scheme is assumed to be stable during the projection period with respect to age, pensionable salary in real terms and past pensionable service.

Regular deterministic valuations of the scheme are conducted during the projection period to determine the current level of funding of the scheme on both a discontinuance and an ongoing basis, and also to determine the future contribution rate required to meet the funding objective. The required contribution rate is calculated in accordance with the Inland Revenue surplus regulations and the Minimum Funding Requirement (MFR) introduced in the Pensions Act 1995.

The effect on the level of funding (and, hence, on the size of the required contribution rate) of using different investment strategies and of varying the pace of funding, by adopting both a traditional prudent valuation basis and a more realistic valuation basis, are also explored.

In this paper we consider a discrete time insurance risk model with interest income. Using the recursive calculation method of De Vylder & Goovaerts (1988), recursive equations for the finite time ruin probabilities and the distribution of the time of ruin are derived. Fredholm type integral equations for the ultimate ruin probability, the distribution of the severity of ruin, the joint distribution of surplus before and after ruin, and the probability of absolute ruin are obtained. Numerical results are included.

Mr Elphinstone, in his recent paper to the Faculty of Actuaries, has reawakened interest in the method of graduation devised by Sir Edmund T. Whittaker some 32 years ago. Except for Professor A. C. Aitken who, in a paper( in the Proceedings of the Royal Society of Edinburgh and a note in the Transactions of the Faculty of Actuaries, gave a brilliant alternative solution of the equations on which Whittaker's method depends, English and Scottish writers have paid little attention to the method. Robert Henderson's paper published in 1924 stimulated American actuaries, and their investigations have continued up to the present time. The book by Kingsland Camp (reviewed J.I.A. lxxvii, 327) gives numerous practical developments of Robert Henderson's work. Students should not overlook a most valuable paper by Charles A. Spoerl which deals comprehensively with almost every aspect of the subject.

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.

Richard Witt's Arithmeticall Questions, published in 1613, was a landmark in the history of compound interest. In a previous paper (J.I.A. 96, 121) I have described the book and attempted to show why it is so important.

This article sets out some information about Witt's life, which has come to light as a result of research done since the previous article (when very little was known about him). Then follows a discussion of some of the books on compound interest which were published later in the seventeenth century. These not only help to fill in the practical background but also show how the techniques came to be more widely known and how problems arose when interest rates were reduced. It is worth noting that there was an average inflation rate of around 1% p.a. during the first half of the century and an average inflation rate of nil, or even a slight deflation, during the second half (Birks & Morrell, 1976; Mitchell & Deane, 1962). Thus, to a very considerable extent, the interest rates used in calculations were real rates of interest.

It is commonly known that in calculating an annuity on three joint lives, two of the lives are made to count as one life of the same annuity value; and that the result is approximately true. Twenty years ago (Phil. Mag., Nov., 1839), I showed that if the law of mortality explained by Mr. Gompertz were accurately true for the whole of life, this substitution of one life instead of two would also be accurately true. I now repeat the same proposition in a more general form.

1.1 Lloyd's and the rest of the London market underwrite a significant part of the world's insurance and are a dominating influence on insurance world-wide. This paper looks at the data which is collected primarily for reserving purposes inside the market—or rather, the paper looks at some new and unusual but very simple ways of looking at that data. Experience is showing that these simple methods are proving to be more powerful aids to underwriters and auditors than was envisaged when they were first invented. They are graphical and hence easy to ‘see’.

1.1. In a recent paper, Pollard(1) introduced the morbidity-mortality table as a model for measuring the interaction between morbidity and mortality of chronic degenerative conditions like breast cancer and lung cancer. This device consists essentially of two double decrement tables: for example, persons either remain free of breast cancer for life or depart from the breast cancer-free group by incurring breast cancer or by dying from other causes; those who incur breast cancer either remain alive with it until they die from it or die from other causes. Clearly this model is very similar to the combined marriage-mortality table which is referred to briefly in U.K. actuarial texts(2). Neither of these models, however, allows for increments, for example recoveries from breast cancer in Pollard's morbidity-mortality table. In recent years one of the major advances in the theoretical development and practical construction of life tables has been the incorporation of increments. A guide to this methodology is provided here with particular emphasis on the measurement of incidence and prevalence of disease. Further applications are given in an accompanying paper, to appear in Volume 111(3).

This paper investigates incentives and disincentives for risk reporting practices by global insurance companies. We examine various arguments for and against risk reporting, whether voluntary or compliance in nature. An important issue is whether reporting is dominated by shareholder, regulatory or managerial incentives. We evaluate whether current reporting practices are consistent with either political visibility, cultural effects or idiosyncratic managerial incentives. Our empirical analysis is based on (1) a content analysis of disclosures contained in annual reports of a sample of European, Asian and US global top 25 insurers between 2006 and 2012 and (2) a survey of internal business reporting practices. We re-characterise a disclosure index from prior research to examine the relation between the extent of risk disclosure and various managerial, agency and other characteristics. We predict that the extent and nature of risk disclosures depends on cultural imperatives and managerial incentives.

This paper examines the political economy of regulation, reviewing market socialist, neo-classical and public interest approaches to regulation and analysing the development of financial services and insurance regulation in these frameworks. However, the paper suggests that these approaches do not capture properly many of the features of a market and the behaviour of regulators. Public choice theory is discussed, and it is concluded that there has not been significant capture of the regulatory process by interest groups. Austrian economics is proposed as a possible framework within which to analyse markets and regulators. It is concluded that there is prima facie evidence to suggest that the Austrian view of the market is realistic and that regulation in insurance markets can have unforeseen and undesirable effects. The author also concludes that, until 1970, insurance regulation did not deviate from principles which are appropriate if either a public choice or Austrian view is taken. However, the Financial Services Act 1998 and the Pensions Act 1995 do deviate from those principles.

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.

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 has two functions: first, in part 1, to present briefly the results of some recent investigations into the behaviour of a price index (in the United Kingdom) in order to gain some insight into the possible future progress of inflation; secondly, in parts 2–4, to present the arguments in favour of the linking to a price index of financial instruments, in particular government stocks, life assurance contracts and pension fund benefits. Part 1 is heavily statistical, and those who prefer the controversial material can go straight to part 2, noting only the conclusion to part 1, viz.: that it is not easy to forecast inflation over any lengthy period. Parts 2–4 are controversial, and I expect will still be topical when the paper is presented. I make no pretence to be impartial; I am convinced that widespread index-linking of long-term contracts would have a beneficial effect on the conduct of our financial affairs. It is up to those who disagree with me to put their case in the discussion; but I hope my supporters will express their views too.