1.1 In recent years, the United Kingdom members of the actuarial profession have become increasingly involved in the general insurance industry and therefore the Institute decided that the subject of general insurance should be included in its syllabus from 1977.

1.2 Prior to 1977 there were a number of papers and articles, written for either the General Insurance Study Group or the Research Committee, on various subjects related to general insurance. These papers and articles have not always had a wide circulation, although they have been deposited in the library at Staple Inn.

1.3 Most of these papers were of an explanatory or technical nature. In the authors' opinion, the actuary has a much wider rôle in general insurance than the technical one of estimating the liabilities of claims. In fact, the actuary should be able to provide a blue-print or framework for the financial management of a general insurance company.

1.4 A general insurance company is a financial concern; therefore the actuarial profession should have a rôle to play. In describing the financial concern, the actuary is required to chart the waters linking profitability, solvency, growth, reserving basis, dividend policy and capital requirements. As the second half of this paper will show, these items are inter-linked and decisions on one should not be taken in isolation as they will have repercussions on one or more of the other items.

The paper compares and contrasts the theories and methodologies of financial economics with generalisations drawn from practical experience of institutional investment management. A Dynamic Equilibrium Model is put forward as a much more realistic theoretical framework than the Sharpe Diagonal Model, a downside theory of risk is developed from sports analogies, and a detailed model of human behaviour, incorporating benchmark levels of ‘unintelligent’, ‘intelligent’, ‘optimal’ and ‘rational’ behaviour, is suggested as a replacement for the very restrictive simplifying assumptions of existing theories. On the basis of a classification system derived from parallels with the history of astronomy, it is concluded that, as a scientific framework, the current theories of financial economics are seriously incomplete, the two crucial areas of incompleteness being the absence of a downside theory of risk and the absence of a realistic model of human behaviour under conditions of risk and uncertainty.

It is proposed to discuss the actuarial problems associated with the management of long-term sickness and invalidity benefits. The emphasis is on benefits provided by social security schemes (with particular reference to National Insurance benefit in the UK), but the main points are relevant to private sector benefits including permanent health insurance (PHI).

The plan of the paper is as follows. We describe in Section 2 the nature of long-term invalidity benefit provided by the British social security system and then consider in Section 3 the problems associated with defining disability. A discussion of the differences between the incidence of morbidity and the making of an insurance claim leads to consideration of selection and moral hazard (Section 4). We then examine in Section 5 the methodology for analysing costs and estimating future costs with particular reference to the development within the Government Actuary's Department (GAD) of a model based on an incidence and survivorship approach to invalidity benefit and the debate aroused by CMI Report No. 7 on the same topic5. The paper then presents an analysis of recent trends in disability claim rates (Section 6) and incidence and termination rates (Sections 7 and 8) based on invalidity benefit within the British social security system, as well as PHI and the experience of other countries. Attempts are then made in Section 9 to explain these trends and the upward trend in financial costs for disability benefits experienced by many social security systems. The paper concludes with an examination of two areas of current interest, viz. sex differences in morbidity rates and claim rates (Section 10) and the relationship between claim rates and the prevailing level of unemployment (Section 11).

1.1 The actuarial profession has for decades, indeed centuries, used age-related tables, particularly (although not exclusively) of mortality, which in preparation have been subjected to the process known as graduation. Five purposes of such graduation have recently been set out by Vallin, Pollard and Heligman and these may be summarized as follows:

(1) to smooth the data, make them easier to handle, remove irregularities and inconsistencies;

(2) to make the result more precise on the reasonable assumption that the real mortality underlying the observations is a smooth curve, i.e. to remove sampling and other errors;

(3) to aid inferences from incomplete data;

(4) to facilitate comparisons of mortality;

(5) to aid forecasting.

Of these purposes, (1), (2) and (3) may all be paraphrazed as implying that the purposes are to make the table smooth, and (4) and (5) as indicating uses to which a table may better be put if smoothed. So the purposes of what the profession has come to term ‘graduation’ all boil down to the production of a smooth table, and for the rest of this paper until the last section I shall use the word ‘smoothing’ rather than ‘graduation’. But what is smooth?

No life has been written of the original projector of the Equitable Society, except in a column of the Biographie Universelle by M. Nicollet. Dodson's name was, and even still is, so familiar to the actuary, chiefly through the Mathematical Repository, and the impulse he gave to life-contingency problems, that this Journal is the proper place of deposit for what can be collected concerning him. The article above mentioned tells very little. He succeeded Hodgson [which should have been Robertson] in the chair of mathematics at Christchurch Hospital in 1756 [1755] and died November 23, 1757. He published the Antilogarithmic Canon, which others had contemplated [and executed too, but the manuscript was lost] and which he had the courage to execute up to a certain point [his table is the counterpart of Vlacq's largest direct table: five figures of argument and eleven of tabular result]. He could not balance the success of the ordinary tables: the writer doubts whether the table was ever used on the continent [he might have added, England: who uses either Vlacq or Dodson? Their tables are for help to other table-makers, and always were, though both of them intended more]. He published, the Calculator in 1747, a collection of tables at the end of which [say in the proper place in the middle] is an abridgment of the antilogarithmic table. But he is best known in England by his Mathematical Repository, and by his zeal for benevolent institutions [say his determination to found an assurance office to which himself should be admissible].

Mortality statistics have now been available for the population of Great Britain for just over a hundred years and during this period there has been a steady and sustained decrease in mortality at all ages and in both sexes, though the extent of the decrease has been progressively less with increasing age.

The main part of the improvement in mortality during the latter half of the nineteenth century was due to improvements in sanitation and hygiene and above all the provision, at any rate in cities, of a reasonably safe water supply. Cholera which occurred in severe epidemic form in London between 1832 and 1866 had disappeared completely well before the beginning of the twentieth century. The widespread epidemics of typhoid fever which occurred as a result of water supplies becoming contaminated with sewage ceased when adequate precautions were taken to safeguard the sources and transmission of water in cities. It is true that small and localized epidemics of typhoid still occur, but these are all found to be due to contamination of food or water by ‘typhoid carriers’. A recent epidemic in Wales, in which some 150 cases of typhoid occurred, was shown to have been caused by the eating of ice-cream which was handled and sold by a man in perfect health but who, following an attack of typhoid many years previously, had continued to pass virulent typhoid organisms in the stools. Fortunately the notification of cases of the disease enables the public health authorities rapidly to track down carriers in this type of epidemic.

This paper investigates the recalculation from its base date of the Financial Times Index of Industrial Ordinary Shares (hereafter called the FT Index) using the ordinary arithmetic mean of the values of its constituents, rather than the geometric mean that is actually used in its calculation. The value of this arithmetic version of the FT Index represents that of a portfolio invested equally in each of the original constituents at the base date. The behaviour of the recalculated index may therefore be described in portfolio terms.

The arithmeticized index has been calculated at each end-year since the base date of the FT Index (1 July 1935). By the end of 1970 its value was 38% higher than that of the (geometric) FT Index. The percentage by which the new index exceeded the original was found to have increased approximately linearly with time; a least-squares linear fit over the whole period indicated that the percentage excess of the arithmetic version over the original index had increased on average by 0·8% a year. A separate fit for the period from end-1960 onwards shows that this rate had increased to 2·7% per year, and even over the period since 1950, it has been 1·1% per year. Use of these relationships gives a rough adjustment of the FT Index for portfolio comparison purposes.

We also calculated a series of arithmetic indices with base dates at the end of each year since the original base date of the FT Index. In the majority of calendar years since its foundation, the FT Index has not fallen far behind the corresponding arithmetic version over the twelve month period. However, over periods of more than a year, the geometric and arithmetic indices can show dramatically different results, particularly if the percentage change in the index value is considered. It is clear that longer-term changes in the value of the FT Index cannot be interpreted as the changes that would have occurred in the value of a portfolio equally invested in the thirty constituent shares at the beginning of the period.

None of these findings affects the usefulness of the FT Index for its original purpose, as a sensitive daily indicator of changes in the industrial ordinary share market. It is purely its long-run use as a portfolio standard that is misleading. For this purpose the more recently instituted arithmetic indices are likely to be useful in the future. Meanwhile, our arithmeticized FT Index values may be useful to correct the downward drift imposed on the FT Index by its geometric construction.

This paper contains an update to the first international comparative study of mortality tables carried out in 2006. It examines the mortality assumptions used in the valuation of pension liabilities in a number of different countries. The results are considered in relation to the underlying population mortality rates, in order to isolate the strength of the mortality assumptions being applied. It is found that there is evidence of a lack of consistency between countries, and that this has not changed since the previous study.

The following notes deal with methods which, although they have been used in various forms for some time, derive special interest from the consideration of the Assurance Companies Act by a Committee appointed by the Board of Trade. In view of the appointment of this Committee, the Council of the Institute felt that a general study of the Act should be made from the point of view of the Actuary, and, in due course, it put forward, among other recommendations, suggestions for improving and simplifying the Schedules. With trifling exceptions, of which, we understand, the particular point under review was not one, there was unanimity among the members of the Council present on the occasions when the Schedules were discussed.

The intention of this paper is to describe, by way of example, how profit testing is carried on in practice and how by making it central to the company's operation the company may be controlled. The mechanism of control is to test the company's results against the results of profit tests built into a model of the company. We shall also describe how the results of these tests of the company's results are fed back into the profit tests to establish the basis for future tests of the company's results.

The motivation for this paper arose from the need to communicate to shareholders the links between profit testing and the company's actual results. It is all very well to say to shareholders that the products satisfy a certain profitability standard but how does that show itself and how real is that profitability paticularly for a new or expanding company which displays nothing but statutory losses or, at best, break even? This communication also led to the need to explain variations from the original projections and finally to answer the question: what happens to profitability if these variances continue?

1.1.1 The Bonus and Valuation Research Group of the Faculty of Actuaries began the work which eventually led to this paper towards the end of 1991. About this time there was considerable speculation that levels of maturity payouts on with profits policies might be significantly in excess of the level that could be justified by the actual investment earnings underlying the policies. The initial aims of the research group were to:

(a) examine this claim;

(b) consider to what extent overpayment, if any, could be explained by the smoothing methods that might have been used by offices; and

(c) examine the practical consequences of continuing to adopt those smoothing methods.

Edmond Halley, who was born in 1656 and died in 1742, is well known generally because of the Comet which bears his name. He is not, however, associated to any great extent with other activities and if it were not for the Comet it is likely that most people today would never even have heard of him. Outside the actuarial profession, and perhaps to some extent even within it, it is not generally known that in 1693 he constructed a life table from the bills of mortality in the German city of Breslau and then went on to calculate from that table annuity rates on one, two and three lives. Reference to this was formerly included in the introduction to the Year Book, but this has now been shortened and the reference to Halley has disappeared.

1.1. This paper is based on the report of a working party set up by the Institute Research Committee and which met for two years from December 1972. The original objectives of the working party were:

(a) to identify current philosophies of bonus distribution in a fund with a high equity content.

(b) to review the methods used for valuing assets and liabilities and the inter-relationship between the respective methods; and to consider the effect of the current philosophies of bonus distribution on those methods.

(c) to investigate methods of valuing assets and liabilities and to carry out research into methods appropriate to modern conditions.

1.2. The working party was not satisfied that it had satisfactorily achieved its objectives but, nevertheless, felt that it should report the progress it had made. The full report is available from the Institute Library together with synopses of some forty papers that were considered relevant. This paper omits the two sections of the report which reviewed current methods of valuation for publication of assets and liabilities and expands other sections in the light of recent events.

Several methods of graduation depend on linear operators–that is, operators of the type …+λ−nE−n+‥+λ0+…+λnEn+… Few attempts have been made to compare these methods, and there is no general theory. There is need for such a theory, for it is easy to show that unless some relation is assumed to hold between neighbouring graduated rates, there is no justification for graduating at all. Any such theory must explain this relation, which cannot be of the simple type that leads to curve fitting.

The paper has two objects : to compare and judge these methods, and to devise a general theory applying to them all.

The first approach is by the classical method–separate examination of fidelity and smoothness.

There has been some discussion in recent years of how best to distribute to with-profit policyholders the benefits which have been derived from investment in equity shares. Normally the practical problem which confronts an office is how to adapt its existing bonus system to distribute these benefits fairly and most of the discussion has been on this problem (as, for example, in the paper by Benz, ‘Some Notes on Bonus Distributions by Life Offices,’ J.I.A. 86, 1).

1.1 The background to the production of this paper is somewhat involved, but is necessary for an understanding of why it contains what it does. Readers who are familiar with recent developments in the valuation field may proceed straight to Section 2.

1.2 Statutory valuations of long-term insurance business under the Insurance Companies Act 1982 (‘the Act’, which superseded the 1974 and 1981 Acts) and the Insurance Companies Regulations 1981 (‘the current Regulations’) have now been prepared by actuaries for some years. Similarly the guidance issued by the profession to Appointed Actuaries, specifically GN1 and GN8, has also remained substantially unchanged over that period. The time was opportune for valuation practice to be reviewed in the light of recent experience.

The Registrar-General's Decennial Supplement 1921—England and Wales—Part I, recently published, is of more than usual interest. It embodies the Report of the Government Actuary, Sir Alfred Watson, who was invited to undertake the task of preparing National Life Tables in connection with the Census of 1921.

In addition to the preparation of English Life Tables No. 9 for Males and Females separately, the only other tables prepared with similar completeness were those relating to Greater London, being the area comprised within the radius of about fifteen miles measured from Charing Cross. On the other hand, the mortality experience of no fewer than twenty-six sections of the country, differentiated by geographical position and density of population, was examined in considerable detail—a feature which, together with others referred to later, distinguishes this investigation from its predecessors.

(1) In a paper read before the Institute in November 1933 (J.I.A. Vol. LXV, p. 38), Mr C. D. Rich showed how to calculate the inherent rate of growth of a population by combining in a single index the current data regarding mortality and fertility. Valuable though this index is in showing the true underlying trend at a particular point of time, it cannot be adapted (nor is it intended) to show the actual future populations at any particular time.

(2) It is the purpose of the present paper to make estimates of the population of Great Britain, according to age and sex, for certain future years, and in order to do this an attempt is made to forecast the probable future course of mortality and fertility in Great Britain, in the light of the experience of the past, and such indications as there may be regarding the factors which will influence the future.

Insurance accounting has for many years proved a challenging topic for standard setters, preparers and users, often described as a “black box”. Will recent developments, in particular the July 2010 Insurance Contracts Exposure Draft, herald a new era?

This paper reviews these developments, setting out key issues and implications. It concentrates on issues relevant to life insurers, although much of the content is also relevant to non-life insurers.

The paper compares certain IFRS and Solvency II developments, recognising that UK insurers face challenges in implementing new financial and regulatory reporting requirements in similar timeframes. The paper considers resulting external disclosure requirements and a possible future role for supplementary information.

Common to all previous studies assessing the cost of adverse selection associated with genetics has been the assumption of an established market, i.e., the adverse selectors have been buying insurance at that rate for such a period that premiums have already absorbed it. Their analyses involve calculating the percentage difference between premiums in a market with adverse selection and one without adverse selection. They can shed no light on how the premiums would get to this stage over time and what losses might be incurred in the process. We take the modelling further by outlining a multiple state Markov model for a start-up market of long-term care insurance. With this model, we explicitly show the progression of adverse selection costs using the development of information that an insurer would gain from analysing the claims history of its existing business, to reprice premiums for new business. To overcome the complication of insurance benefit amounts, which depend on the value of previous benefit payments, we develop a simulation approach of estimating the expected present values of insurance benefits and premium payments. In applying our modelling to a UK setting, we find genetic testing of the apolipoprotein E gene (whose variants can cause a high risk of developing dementia) to be of a relatively small impact compared with our hypothetical state of intermediate dementia progression. Furthermore, we find that the government’s cap on care costs has little effect on adverse selection costs as it benefits only a small proportion of people.