Almost a quarter of a century ago—in 1958 to be precise—one of my predecessors devoted the main part of his Presidential Address to a discussion of state and occupational pensions. He spoke at a time when price inflation was 2¾%, growth in the national income had been averaging 2% p.a. in real terms and the number out of work was half a million. The redemption yield on long-dated Government stock was about 5¼% and the dividend yield on the Actuaries' Investment Index of Ordinary Shares was 5¾%—we did not yet have the reverse yield gap that recognizes the endemic nature of inflation.

1 Whichever way you look at it, pensions are a problem. The Policy Studies Institute has expressed concern at the increased burden of State pensions fifty years from now when the number of pensioners increases in relation to the number of contributors. The Institute for Fiscal Studies too is anxious for the same reason and makes the criticism that insufficient consideration was given to the long-term cost when the State scheme was extended in 1978 so as to provide an additional earnings-related pension. The report of the Scott Committee has reduced but not wholly eliminated controversy on the extra value of index-linked public service pensions compared with the pensions commonly provided in the private sector. Employers, on whom the financial burden finally rests, are hard pressed to finance the accrued pension rights of their employees in final salary pension schemes and are unable to make the additional contribution necessary to preserve the values of the pensions and deferred pensions of former employees.

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 paper reports the results and conclusions of a project which provided a statistical analysis of survival after stroke (or cerebrovascular disease) and derived appropriate life assurance underwriting ratings. The methodology used has been described elsewhere and will be referenced as needed.

The project forms a pilot study set up to consider the feasibility of collecting and analysing in detail the considerable medical and actuarial literature that has accumulated on the prognostic experience of impaired lives over the last 30 years.

Let E be an event whose probability of occurrence depends on some continuous variable x, P(E|x) = qx

For example, E may be death and x age, E may be incidence of lung cancer and x amount of smoking, or E may be reconviction of a parolee with x previous criminal convictions (with suitable definitions of the underlying time interval for the occurrence of E). Given observations on n individuals with characteristic x and the incidence of E, it is desired to estimate the function qx.

The simplest case is when the data are grouped—suppose x occurs in nx cases of which E occurs sx times. Then the elementary crude estimate is

This paper describes a simple, non-parametric method of graduating observed rates or probabilities of the form The technique has been used for smoothing data sets arising in medicine and criminology (Copas(1)(2)) and is extended here to an actuarial example and the results compared with more traditional approaches.

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).

1.1. This paper describes a consistent and justifiable means of establishing adequate claims provisions in General Insurance. The topic has created widespread interest amongst actuaries, accountants and regulatory authorities. The issue of adequate provisions is of utmost importance to policyholders, whose justifiable claims must be paid, insurance companies who must be able to satisfy shareholders and make proper assessments of premiums, and regulatory authorities who must be satisfied that adequate provision has been made for all liabilities.

This paper finds a strong size effect for the total business of 106 U.K. life companies from the 1981–82 Insurance Directory and Year Book.

The industry is regulated by the 1982 Insurance Companies Act which consolidated earlier legislation. This does not control output or prices of firms but many other items including investment. The industry is not highly concentrated with the five largest firms in 1980 with 30% of premiums. In 1980, total ordinary branch premiums amounted to £5.8 billion.

Section 2 surveys briefly some relevant research, while §3 discusses the data and size and other economic factors for life assurance firms. Section 4 discusses the empirical results while §5 has a brief conclusion.

The increasing involvement of Australian governments and people in social welfare and the increasing number of histories appearing in this field, makes it appropriate to recognize the alternate institutions—the mutual-aid bodies. By looking at these private institutions, which began to develop in the nineteenth century, we gain some perspective on the initiatives of government in the twentieth century in social policy in Australia. This paper does not extend to banks, building societies or to other co-operatives, but is restricted to those two institutions, friendly societies and the life insurance companies, which sought to provide for the exigencies of sickness, old-age and death.

For most people, statistical forecasting means modelling time series using the methods described by Box and Jenkins (1970). A Box and Jenkins model requires a large number of known data points before it can be properly chosen and, since it cannot be changed without again observing another batch of input, is only of use if the data conforms in the future to the chosen model. This means that this style of forecasting is essentially rigid, unadaptable and of limited use in practice. This paper sets out, with the aid of the examples, the essentials and some applications of Bayesian forecasting as developed by Harrison and Stevens (1976).

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.

1. In the three years since projections of occupational pension scheme membership and expenditure were made for the Wilson Committee more data about schemes has become available, such as that from the Government Actuary's survey of Occupational Pension Schemes 1979 (the G.A.'s Survey), so the occasion of the publication of the Government Actuary's National Insurance Fund Long Term Financial Estimate (the Quinquennial Review or Q.R.) has been taken to revise and extend the Wilson Committee projections, using the starting date and earnings and prices assumptions of the Q.R.