State Pension Age (SPA) is an issue of topical interest in the United Kingdom at the time of writing owing to the Government’s plans to link SPA at future dates to estimates of the projected longevity of the population. This paper considers the background to the current position, how the linkage is proposed to work, other factors that may need to be considered and some changes in the proposed State pension regime that could be alternatives to, or complementary with, a changing SPA.

In this paper it is demonstrated how recently developed statistical techniques designed to facilitate the joint modelling of the mean and dispersion are well suited to model the presence of duplicate policies in graduation.

Forecasts of mortality are included in official population projections. The methodology and performance of British mortality forecasts is reviewed and compared with those of the United States of America in the quarter century up to 1989. The results are found to have been surprisingly poor when compared, for example, with the more widely-criticised fertility component; similar conclusions hold for other developed countries. Although the methodology has become more sophisticated over the years by using detailed information on cause of death and cohort-based approaches, this has not led to obviously better forecasts, and the time period at which the forecasts are made is more important than the method used. The particular importance of mortality assumptions in determining projected numbers of elderly people discussed.

The paper describes the philosophy of with-profits business which has been developed in the authors' office, as a practical illustration of the running of such business in modern conditions. A description is given of how the philosophy is implemented in the main areas of actuarial management, including valuation methods, bonus distribution, product design and expense control. The discussion is extended to address a number of topics which are the subject of current debate including the financial strength of offices, future bonus prospects and disclosure of expenses.

In a series of trials with constant probability p of ‘success’ (S) and q ( = I–p) of ‘failure’ (F), the problems arise of determining the expected number of trials required to obtain a specified pattern of results (e.g. SSFSFFSSSFF), and of calculating the probability that such a pattern will appear in a given number of trials. We are here concerned essentially with ‘general’ patterns which may exhibit no clear regularity; many methods are available, and well known, for dealing with regular patterns (e.g. SSSSSS or SFSFSF), which do not apply to irregular ones. Feller, has shown how to solve the problems for general patterns, using an ingenious definition of the event corresponding to the appearance of the pattern whereby it becomes a recurrent event; his powerful general theory of recurrent events then applies and yields the required information by means of generating functions. A different method is given on page 171 of Bizley for finding the expected number of trials required to obtain a general pattern; this uses only the simplest mathematical tools but involves rather a lot of work for long patterns. Under each of these methods, however, every given pattern has to be treated individually and a separate calculation performed.

Risk terminology varies from organisation to organisation, and actuaries working in different organisations may use different terms to refer to the same risk, or use the same nomenclature for completely different risks. This paper sets out a classification system developed by the Risk Classification Working Party for the Profession that can be used as a common reference point for discussing risk. Actuaries will not be required to use this system, but it is hoped that common terminology will reduce the possibility of confusion in discussing risks.

This paper explores the effect of unhedgeable background risks such as mortality and labour risks (such as wages and turnover) on pension funding and finance. We explore the literature on the economics and finance of background risk, and discuss its applicability to pensions. Most of the results in economics apply to the special case of additive background risk, which is part of, but not all of, the background risk faced by pension funds. We develop three illustrative models and show the impact of background risk on pension funding and asset allocation. We find that the asset allocation and funding decisions of pension plans in general change with the introduction of background risk, in some cases significantly. We also explore implications of background risk for fair value calculations.

Tuberculosis at the present time still causes over 20,000 deaths a year in England and Wales and is one of the major medical problems of the day. The mortality of the disease has been considered several. times recently in papers or discussions of the Institute (Pedoe, 1947; Elderton, 1947; Conybeare, 1948), and always it is the mortality by calendar years that has been mentioned or implied. It is the purpose of this note to draw attention to the somewhat different picture obtained when generation mortality rates for tuberculosis are examined.

The pattern of mortality at the highest ages has been considered by many authors, including Redington (1969), Humphrey (1970) and Benjamin (1964, 1982). The questions raised have included the following:

(a) Is there a definite upper limit to the span of human life, so that qx reaches unity at a finite age? Or does qx tend gradually to unity as age tends to infinity, as happens under the Gompertz and Makeham laws? Or does qx tend to a constant less than unity, as under the Perks formula or the formula which was used to graduate the English Life Tables No. 11 and 12?

(b) Has the fall in mortality rates at lower ages been accompanied by a similar fall at the very highest ages? Has the upper tail of the curve of death (μxlx) shifted?

(c) Does the lower mortality of females compared with males extend to the very highest ages, or do the rates eventually tend to converge?

This paper is a report from the Extreme Events Working Party. The paper considers some of the difficulties in calculating capital buffers to cover potential losses. This paper considers the reasons why a purely mechanical approach to calculating capital buffers may bot be possible or justified. A range of tools and techniques is presented to help address some of the difficulties identified.

The paper first considers concepts of profit in economics, accountancy and the law relating to financial reporting. It then considers the nature of life assurance business and suggests the accounting standards appropriate to life assurance companies which would ordinarily result in accounts showing a ‘true and fair view’. An analysis of the E. C. Insurance Accounts Directive shows that there may be circumstances where its provisions conflict with such standards.

The paper considers each of the statutory solvency method, embedded value reporting and the accruals method, and the author finds all of them to be inconsistent with accounting standards and the requirements of the Directive.

The author puts forward the ‘Earned Profits’ method, which applies accountancy principles in determining assets and liabilities and takes credit for outstanding revenue matching acquisition costs. This approach is then used in analysing the value of a life assurance company and measuring the rate of return on capital.

1. The development of this paper involves the consideration of certain arithmetical, mechanical, and photo-electrical technicalities, but the ultimate aim is a very simple one and it may therefore be advisable to state it at once. The ultimate aim is to persuade the whole civilized world to abandon decimal numeration and to use octonal numeration in its place; to discontinue counting in tens and to count in eights instead.

This paper looks at alternative long-term care (LTC) funding models and options. It analyses six global models and the potential applications to the United Kingdom. The paper provides a demographic overview for each of the six countries to illustrate the increasing global demand for LTC and the funding thereof that is becoming a global critical issue. It examines the approaches each country has taken to address the funding issue with varying degrees of public/private co-operation and partnerships. The authors hope that the lessons learned from these other markets will assist the United Kingdom as they try to come to grips with their growing social care funding issue.

A great deal of research has been carried out into expected values of qx or into expected number of deaths. Little attention has however been paid to the random variations in mortality rates or to the random variations in the number of deaths. Research in this direction might very well further our knowledge of the mortality process.

1.1. The work for the paper was carried out by the authors as members of the Bonus and Valuation Research Group of the Faculty of Actuaries. The previous paper produced as a result of work done in the Bonus Research Group (Studies of Reversionary Bonus using a Model Office, TFA 37, 91) used a deterministic model office. Future interest rates and returns from equity investment were assumed known and the effects on reversionary bonus of variations in the valuation bases, rates of expansion and inflation of expenses were examined. The assumption of an exact knowledge of future investment returns was a great simplification and begged many of the important questions facing a life office actuary. In this paper the Research Group has paid attention to the change in the value of the assets under variations in financial conditions.

The purpose of this short note is to explain a simple method of constructing a life table, given an explicit function for the force of mortality, μx, for all x. A similar method can be applied to the construction of multiple decrement tables, given explicit functions for the separate forces of transition, μbx, μcx, etc, from one ‘active’ status (a) to various ‘dead’ statuses (b, c, etc) for all x.

Although numerical results for the examples discussed in this note could be calculated equally well by more direct methods than the ones described herein, results for more complicated examples involving multiple status tables, in which transition back and forth between statuses is possible, cannot in general be calculated by such direct methods, and our methods provide a practical way by means of which numerical results for these more complicated cases can be calculated.