I cannot recall that national fuel policy has ever previously been the subject of a paper to the Institute, though it is becoming quite usual for the Institute to address itself to subjects outside the traditional actuarial fields. Nearly all the Alfred Watson Memorial Lectures, for example, have been on outside subjects and two of these, ‘Some thoughts on economic forecasting’ by Sir Alexander Cairncross (as he is now) and ‘Problems in forecasting in the chemical industry’ by Sir Paul Chambers, have certain links with the subject of this paper.

1.1 Medical expenses insurance, as we know it today, has been available in the United Kingdom since the late 1940s. In recent years the market has increased significantly to a point where we estimate approximately 6m people are now covered by medical expenses insurance, which represents over 10% of the population. Furthermore, there is evidence that the market is continuing to expand.

The two-fold purpose of this paper is:

(i) To hypothesize the existence of a Basic Curve of Deaths, a curve to which it is suggested all curves of deaths are, as it were, striving to attain—the ‘idea’ of a curve of deaths, almost in a Platonic sense, a curve applicable not only to humanity, but equally to all forms of life.

(ii) To seek a representation of that curve by a function containing as few parameters as possible, on the principle that while there are other functions which fit the observations more exactly, we here prefer a simple function which fits them well enough.

1. The finances of life offices have been discussed by actuaries for more than a century and it seems entirely safe to predict that these discussions will continue into the future, with no diminution either of enthusiasm or of topics of general interest. The developing nature of many of these topics needs no emphasis, either from the viewpoint of changing external circumstances, or of the length of time which has elapsed since the first mention; for example, bonus reserve valuations were referred to in an Institute discussion nearly a century ago, investments in ordinary shares were mentioned before the close of the last century and variable assurances were touched upon over 30 years ago.

The draft paper sets out the authors' views of what good practice for the actuarial aspects of internal models will look like in 2012, the year Solvency II is expected to be implemented. Actuaries working on internal models can expect to have to follow such practices if their internal models are to be approved for use in calculating regulatory capital. The paper is therefore relevant for actuaries who plan to work on internal model implementation for Solvency II.

Moreover, the risk quantification techniques discussed in the paper can also be used in the Own Risk Solvency Assessment (ORSA) process also required by Solvency II. The paper is therefore relevant to actuaries working in companies that are not planning to apply to use an internal model.

The paper covers both life and non-life insurance and reinsurance, and reviews current practice as well as setting out possible future practice. This leads to identification of areas for research by the Profession to prepare for 2012 and an indication of the directions this work might take.

The paper is effectively a work in progress, and readers should ask themselves what they should do in response to the ideas discussed.

Schedule 1 of the Insurance Companies Act 1982 defines Permanent Health Insurance (PHI) as a class of Long Term insurance business being “… contracts of insurance providing specified benefits against risks of persons becoming incapacitated in consequence of sustaining injury as a result of an accident or of an accident of a specified class or of sickness or infirmity being contracts that:

(a) are expressed to be in effect for a period of not less than five years, or until the normal retirement age for the persons concerned or without limit of time, and

(b) either are not expressed to be terminable by the insurer, or are expressed be so terminable only in special circumstances mentioned in the contract.”

The fundamental features of PHI as developed in the U.K. are therefore:

(a) It provides specified benefits in the event of ill health.

(b) Cover may not be cancelled by the insurer (except under special circumstances described in the policy document) and hence the insurance is ‘permanent’.

Actuarial models of the market in conventional British Government Stocks, also known as the Gilt-Edged market, are reviewed and contrasted with the methods which have been developed, during the last twenty years, by financial economists.

Following the Treasury's announcement in May 1995 (regarding the taxation of institutional bond holdings), the so-called ‘coupon effect’ has largely disappeared and gilt prices can now be fitted very closely by using the same simple discounting functions for both income and capital flows. A new model suitable for the calculation of yield indices is proposed and is contrasted with the model currently underlying the FTSE Actuaries Government Securities (FTSEAGS) Yield Indices. A number of new possible applications of the reformulated yield indices, such as forward pricing, asset/liability matching and stochastic simulation, are discussed. An analogous model for index-linked gilts leads to applications involving the forward market in the retail prices index.

A survey of professional users of the FTSEAGS Indices is described, and a revised presentation for the published yield indices is suggested. A summary of current statutory references to the indices is presented.

Statement of Standard Accounting Practice (SSAP) 24 required, for the first time, particular levels of disclosure in relation to firms’ pension arrangements. Whilst this was a major step forward, it allowed a significant degree of discretion. This discretion meant that SSAP 24 was an observable measure of the quality and quantity of accounting disclosure for firms. This information can be used to determine the types of firms that give less information or use weaker assumptions. In my analysis, I find some evidence that large firms give more complete disclosures, but also that they are more able to exert influence on their actuaries to use weaker assumptions for the valuation of pension scheme liabilities. There is also some evidence that more profitable firms disclose less, so firms with a higher average tax rate might want to overfund their pension scheme. Finally, there is evidence that highly levered funds are less likely to give complete disclosure, and that when they do disclose their assumptions, they use a weaker basis.

The paper is concerned initially with the admissibility of particular claim payment models. Admissibility is restricted by the requirement that, if claims escalation is excluded, the amount of outstanding claims at any epoch of development of a generation of claims should be independent of the future speed of finalization.

This simple requirement represents an invariance condition. The problem of admissibility of models can therefore be approached in the manner of invariance problems in physics. Standard techniques of variational calculus are used.

The theory of Probabilities has been characterized by Laplace, one of those who have contributed most largely to its advance,—as “good sense reduced to a system of calculation;” and such, no doubt, it is. But it must be especially noticed that there is hardly any subject to which thought can be applied, which calls for so continuous an application of that excellent quality, or in which it i s easier to make mistakes from simple want of circumspection. And, moreover, that its reduction to calculation is attended with difficulties of a very peculiar nature, such as occur in no other application of mathematical analysis to practical subjects, arising out of the great magnitudes of the numbers concerned, which defeat the ordinary processes of arithmetical and logarithmic calculation, by exhausting the patience of the computer, and require special methods of approximate evaluation to bring them within the compass of human industry. These methods form a conspicuous feature of the general subject, and have furnished scope for very extraordinary displays of mathematical talent and invention. That very large numbers will inevitably be concerned in questions where numerous and independent contingencies may take place, and in any order or mode of combination, will be apparent to any one who considers the astonishing fecundity of such combinations numerically estimated, when the combining elements are many. For example, the number of possible “hands” at whist (regard being had to the trump) is 1,270,027,119,200.

In considering the origin and development of the friendly society system, it is necessary to recognize the twofold purpose that these institutions have fulfilled. In the view of the actuary they are merely associations for the mutual assurance of certain benefits, generally in the case of the sickness or death of any of the members. This, however, represents only one side, and that by far the most recent, of the work of these institutions. A not less prominent and much older feature is to be found in the opportunities for social intercourse, companionship, and mutual help, which such associations naturally afford—wants common to man in every state of society, and as old as civilization itself. Hence, from the earliest times, small communities have existed, drawn together by the common interests, tastes, or pursuits of the members, such communities being originally purely social in character, subsequently charitable and mutually protective, and only in recent times financial.

The Working Party has developed some practical hints and tips for those developing integrated risk management (IRM) plans for UK defined benefit pension schemes in the context of the requirements of the Pensions Regulator. Four case studies are presented to illustrate its conclusions, which are encapsulated in the ten commandments for effective IRM. IRM is the consideration of investment, funding and covenant issues, and how these interact. Its purpose should be to aid decision making and so should have a clear outcome in mind. It should be a continuous process and should form part of everyday trustee governance – it is not simply a one-off exercise. Whilst most Trustees and advisors consider funding issues when setting their investment strategy and vice versa, fewer fully integrate covenant into their decision-making process. However, covenant underpins all risk taken in a pension scheme and so needs to form a regular part of trustee discussions and analysis by advisors.

We have chosen Investment Policy and Index Numbers as the title of this paper, because the origin of the Actuaries' Investment Index is to be found in a paper, The Statistical Groundwork of Investment Policy, by the late C.M. Douglas (T.F.A. 12, 173).

The main policy consideration discussed by Douglas was the extent to which offices should invest in equities. Douglas maintained that funds should only be invested in equities if greater security was thereby obtained. To establish the suitability of equities, it was necessary to study the relative variations in equity prices, debenture prices and business activity. For this purpose, index numbers were required.

From a study of index numbers covering the period 1924-28 Douglas concluded that share prices were related to the level of business activity, i.e. to the progress of the ‘trade cycle’, equity prices following the cycle directly, and debenture prices following the cycle inversely, but with a different tempo and interval. If, therefore, an investor could judge the future trend of business activity, a sound investment policy could be pursued.

In this paper we propose to review some of the developments that have taken place in the principles and practice of investment policy over the last twenty-five years, and to study the contribution to these principles that the Actuaries' Investment Index and other index numbers can provide. In addition, we propose to review the methods used in the construction and maintenance of the Actuaries' Investment Index in the light of current conditions.

The paper deals with the development of unitised with-profits business in the United Kingdom. The authors trace the recent history of these products and comment on the main reasons for their development They also deal with corporate issues, including implications for policyholders and shareholders of different fund structures and different types of life office. Pricing and product development issues are also covered. Reserving issues including the range of valuation methods, statutory requirements and policyholders' reasonable expectations are explored. Finally the paper considers the actuary's contribution to the management of unitised with-profits policyholders' expectations.