The values of the returns of past and future contributions on death before retirement, such contributions being accumulated to the date of death at rate j, are given respectively by

(TPC)xPCFx and (AC)xFCFx

where (TPC)x=total past contributions at age x accumulated with (compound) interest at rate j to the valuation date,

(AC)x = actual annual contributions payable at valuation age x.

This paper focuses on sections of the insurance industry which are not often widely discussed. If catastrophe insurances are to be transacted successfully, a large number of different technical skills and experiences must be combined. Actuaries in the U.K. are still relatively little employed on the problems of general insurance, and are rarely involved in the complexities of these particular sections of it. It must be recognized that there is only limited scope for the application of actuarial skills in this field. However, there may be some advantage to be gained by mixing an intelligent statistical opinion with other specialized technical or practical ones when some catastrophe problems are being discussed. Before expressing a view on any topic, it is, of course, essential to learn about the background and existing conditions.

The concept of catastrophe is considered in section 2 of this paper. Potential catastrophe situations can be classified into two groups, natural hazards and man-made hazards. Each of the sections 3–9 deals with one of the principal natural hazards, giving an outline of the causes of catastrophic events, the type of losses to be expected, and the form of insurance cover likely to be available in vulnerable areas. Section 10 describes the New Zealand state scheme, which provides cover in the event of extraordinary losses from nearly all elemental perils, and war. Sections 11–16 each deal with a different type of situation where a man-made catastrophe can occur, and the insurance provisions available in each case.

This paper overviews a practical approach to the assessment of operational risk in life insurance companies. It considers how actuaries, working in conjunction with risk management professionals and senior management, can develop a framework to assess the capital requirements relating to operational risk, taking into account the capital requirements of other risks and their interaction.

This paper recognises that we do not live in an ideal world, and that a lot of the data which one might want for operational risk assessment are not, and in some cases never will be, available. Consequently, the approach outlined in this paper takes into account the fact that management and assessment of operational risk is at an early stage of development in the life industry. In addition, it outlines some of the areas where development is necessary or desirable in the coming years.

There is a section on the operational risks against which it is appropriate to hold capital. As this is a new area for insurance companies, and given the governance requirements for Individual Capital Assessments, it is important to explain the results effectively to senior management. Therefore, a brief review of techniques for reporting the results of the assessment is provided.

The paper concludes with some thoughts on how operational risk management can be embedded more in the business, and then considers what future work will help develop the framework. To echo the thoughts of the authors of the general insurance paper on this topic (Tripp et al., 2004), we hope that the paper will sow seeds for the development of best practice in dealing with operational risk, and will raise the awareness and increase the interest of actuaries in this emerging topic.

This paper represents the views of the individuals in the working party, and not necessarily the views of their employers or the Actuarial Profession.

Although much has been written in recent years on the comparative merits of different methods of valuation, I am not aware that any attempt has yet been made to ascertain the ultimate bearing on the Pure Premium Method, of the facts that have been recently brought forward as to the pressure of the expenses and the effects of selection in an assurance company. Speaking generally, it will, I think, be found that proposals to diminish the pure premium reserve on account of the necessarily heavy expenses of new business, have been made without reference to the mortality profit that may be expected to arise from the recent selection of the lives, and vice versa. This being the case, it occurred to me that it might be of considerable practical interest to make an investigation in which effect would be given to the influence both of expenses and of selection, for it would enable us to estimate how far the one neutralized the other. In order to render the inquiry more clear, however, it will be well to begin by considering each separately.

The application of sampling technique to statistical data, which a few decades ago was a rarity, has now become common practice. Our past President, Mr F. A. A. Menzler, in his presidential address said:

Sampling, in all its manifestations, has become almost a social and industrial routine. In this paper, by examining in some detail the application of sampling to a particular branch of actuarial work, namely pension fund valuations, an attempt is made to investigate the possibilities of its use in the actuarial-field. By the choice of pension fund valuations, which are a particularly complicated example of the actuarial technique, the investigation will, it is hoped, give a good insight into the sort of problems involved.

1.1 The price of a particular ordinary share represents an equilibrium position between the views of those participants in the market who wish to buy and those who wish to sell. Most participants, and certainly all institutional investors, have access to a vast amount of background information, and share prices adjust continuously as these participants revise their buying or selling prices in the light of new information or in the light of a changed interpretation of existing information. If an explicit price model can be developed solely from the principle that prices are in equilibrium once all participants in the market have acted on their interpretation of the information available to them, this model will be of considerable assistance in the management of ordinary share portfolios.

1.2 This paper describes the construction and application of such a price model and discusses the optimal extent to which mathematical and statistical methods can be employed in portfolio management. A recent paper by Clarkson (1980) describes the stage of development that had been reached at the end of 1978; the present paper expands on the underlying concept of market equilibrium and on the practical implications for the management of institutional portfolios of ordinary shares.

The introduction of high-speed electronic computers has opened the way for analyses of motor insurance risk statistics on a scale not previously possible. We may regard the purpose of the analyses which form the subject of this note as being to test the validity of the existing rating structure by finding out how the claims experience varies from one rating cell to another within that structure; and, more generally, to explore the possibility of devising a more efficient rating structure by defining new levels within the existing factors, or by using new factors in addition to, or in replacement of, those already used.

To achieve this purpose it is appropriate to consider on the one hand a detailed investigation of the experience over a limited period, analogous to that carried out when constructing a new standard life table and, on the other hand, a system for keeping the emerging experience under more or less continuous review. For this second aspect it is natural to think in terms of making comparisons between the actual experience and that expected according to the standard table.

In 1900 life expectancy at birth in the UK was only 46 years for men and 53 years for women. Just over a century later life expectancy at birth has increased by around 30 years and by 2007 had reached 77.5 years for men and 81.7 years for women. The population aged 85 years and over, often termed the ‘oldest old’, are now the fastest growing section of our population. For the 1921 cohort only 18% of men and a third of women reached the age of 85 years but for the 1951 birth cohort it is expected that almost half of men and 60% of women will achieve that age. The important question for health care planners and society is whether the large number of those who will reach 85 years in the future are similar in health characteristics to those attaining 85 years now.

This question was addressed by substantive results and by methodological papers in the ‘Cohort’ theme of the Joining Forces on Mortality and Longevity conference in October 2009. Here we provide an overview of the papers, some of which are presented in full in this issue (see Murphy (2009), Di Cesare & Murphy (2009), O'Connell & Dunstan (2009), Forfar (2009)).

The text of this paper, together with the abstract of the discussion held by the Faculty of Actuaries on 19 March 2007, are printed in British Actuarial Journal, 13, III, 479-555.

Lord Kelvin many years ago expounded his oft-quoted dictum, ‘When you can measure what you are speaking of, and express it in numbers, you know that on which you are discoursing. But when you cannot measure it or express it in numbers, your knowledge is of a meagre and unsatisfactory kind.’ Operational Research is primarily concerned with measurement in management.