The original Actuaries Index was designed in 1929 and was maintained with broadly the same format and principles for more than thirty years, changes to constituents and groups being made in 1950 and 1957. Investment Policy and Index Numbers, submitted by the authors in 1956 (J.I.A. 83, 333), discussed the original index in some detail. This index was, of course, designed for manual calculation and it is remarkable that only eight years ago electronic computation was not even contemplated. In fact the word computer was never mentioned in the paper or in the discussion. With electronic facilities now so well developed the whole approach to indices is changed. The limitations, formerly imposed by manual calculation, on the size, the scope of the averaging procedures and the weighting methods, and the frequency of computation are no longer important.

The first part of the Address is a review of changes over the last 30 years in the actuarial management of a life office — ranging from the introduction of the Appointed Actuary system to some of the consequences of the Financial Services Act. It draws attention to some of the differences in the regulatory treatment of life assurance companies and other competing organisations in the savings field, highlights some of the shortcomings in the European solvency regime that is currently being reviewed by the authorities, comments on developments in the area of anti-discriminatory legislation and draws attention to some possible problems arising from such legislation.

The Address continues by outlining some of the issues that must be tackled if the profession is to expand into other fields, and the last part comments on developments in the day-to-day management of the United Kingdom actuarial profession and the Faculty's relationship with the Institute.

A careful study of the prospectuses of the leading life offices discloses so great a variety of practice in minor details that the question naturally arises whether something cannot be done to secure uniformity. I propose in the following pages to discuss a few illustrations of this diversity of practice with a view to showing that the requisite combination on our part could not fail to exercise a beneficial influence by the simplification of a naturally complex branch of business, by the withdrawal of unnecessary and vexatious restrictions, as well as by the resistance which could be offered to the demands for unwise concessions.

In a paper on Large-scale Electronic Digital Computing Machines read before the Institute in 1953 (J.I.A. 79, 274) R. L. Michaelson drew the attention of actuaries to the possibilities which existed in a life office for the use of a large-scale electronic digital computer (referred to hereafter as a ‘computer’). Both the paper itself and the discussion which followed emphasized the need for a detailed investigation of the problems involved from the points of view of the life office and the manufacturer.

2. The author of this paper has been privileged to undertake, in close cooperation with a large manufacturer of computers in this country, a detailed investigation of possible life-office organization based on a computer. This paper sets down some of the results of this investigation with particular reference to life offices transacting ordinary as distinct from industrial life assurance.

The recent financial crisis has raised challenges to market-consistent valuation, both in its implementation and application. These include both commercial and technical challenges. The whole concept of mark-to-market accounting has been questioned in some quarters.

There have been commercial challenges in deciding how to assess business strategies given recent volatile market-consistent results, including the implications for ALM and new business pricing. Industry-wide, macroeconomic concerns have been raised regarding procyclicality.

This paper recognises these commercial challenges and highlights how a combination of different forms of management information covering both market-consistent and other measures can help in making decisions. This paper sets out some possible approaches to mitigate procyclicality.

There have been technical challenges in:

• – assessing how to value instruments in markets which are or have become illiquid

• – selecting an appropriate ‘risk-free’ or reference rate

• – deciding whether and how to make additional allowance for the liquidity premium or own credit risk

• – the calibration of stochastic models used to value embedded financial options and guarantees

• – assessing an appropriate allowance for non-hedgeable risk.

This paper discusses these technical challenges. The paper proposes a way forward in some areas, taking into account the recent dislocation of the financial markets and drawing on recent Solvency II, IASB, FASB and MCEV developments.

After the publication of the volume of statistics of the data derived from the Continuous Mortality Investigation 1924–29, experiments were made by the author in fitting the curves developed by Perks in 1931 (J.I.A. LXIII, 12) to various sections of the data. The experiments were later extended to include the data for the Light and Heavy tables and the experience for the period 1924–38. Although these experiments are now mainly of historical interest they represent useful material for research in testing and otherwise and, together with the results of some other published and unpublished graduations, they form the background of this paper.

Conventional diagnoses of the 2007/8 Global Financial Crisis see it as “abnormal”, and then resort to explanations in terms of “irrational exuberance”, “animal spirits”, “herding behaviour” and so on. The prescription – “better regulation” – then follows automatically, as it has done after every such crisis, all the way back to tulipmania 400 years ago. But if there are different “seasons of risk”, and if financial sector actors are able to latch onto different risk-handling strategies, each appropriate to one of those seasons and inappropriate to the others, then we have a very different explanation: one in which, in contrast to both neoclassical and behavioural economics, rationality is no longer singular. This “anthropological” hypothesis has its roots in Mary Douglas’s book “How Institutions Think”, and the paper shows how it is well supported by historical evidence, agent-based modelling, and fieldwork among both financial sector firms and their regulators, as well as by parallels from ecology, organisation theory and evolutionary (i.e. Schumpeterian) economics.

In Australia, the Insurance Acts 1973 introduced the formal requirement of a solvency margin. The solvency margin required by Statute is a proportion (15% in fact) of net premium written in the last completed financial year. Since then, there has been a certain amount of discussion on the means of funding that margin under expansionary conditions.

The vicissitudes of the discussion in Australia and the United Kingdom have been as follows.

At first, it appeared unquestioned that increases in solvency margin must be financed effectively by premium loadings. For example, Loader and Ryder (1976) state flatly that “The increase in solvency margin must be met from profit earnings”. The ideas of Loader and Ryder were adopted as a point of departure by Cooper and Long (1977). Basically the same theme was presented by Eriksen and Jones (1977).

The paper surveys the present state of knowledge about the appraisal and control of capital projects, and identifies the useful contribution which actuaries can make to the process.

Relevant theoretical considerations are discussed, including the choice of appropriate discount rates for use by companies when screening proposals. It is recommended that discount rates should be lower than those commonly used. Some practical working methods are summarised and examples are given of how risk analysis can be carried out, for both simple and complex appraisals. Attention is drawn to the special ‘social’ considerations which may apply in the case of Government projects. The opportunities now opening up for joint ventures between the UK Government and private sector partners are examined, and it is concluded that proper sharing of costs and risks can facilitate arrangements which are acceptable to both sides.

The paper concludes with a discussion of the procedures which companies can use to identify, appraise, control and monitor projects.

Let θx, denote the number of deaths (from all causes or a certain cause) at age x last birthday arising from the central exposed to risk Ecx. We show that, under certain conditions, θx, has approximately a Poisson distribution with parameter

where μy denotes the force of mortality at age y. This result is applied to find confidence intervals for the true central death rate, to estimate the distribution of the cost of claims and the expected death strain.

The frequently-used actuarial formula

where A is the actual deaths and E the expected deaths, is found to hold in large investigations, as is the alternative (but generally less accurate) formula

By the assessment of life-risks, I mean the gathering together all the scattered influences that bear on the duration of life of particular individuals; the connoting in the mind the weight to be attached to the several factors that make up such influences; and, finally, the fixing the price of assurance for each individual life which approximately puts all upon a level.

This paper addresses the fundamental issues in the construction and use of actuarial economic models, with specific reference to those described in the UK literature. Two approaches are considered: an empirical approach and a theoretical approach using financial economics. Although empirical testing is essential, the difficulties associated with it should not be underestimated. A theoretical framework can be used to limit the impact of these difficulties. However, economic modelling is further complicated by the lack of a reliable and comprehensive theoretical framework. This suggests that economic models are always likely to be inaccurate and consequently actuarial judgement is likely to be indispensable.

One of the most powerful devices in the theory of compound interest is Makeham's formula. The essence of the formula may be stated as follows:

Consider an admitted loan of C bearing interest at rate g per annum (payable pthly in arrear) per unit of admitted capital. The loan is to be repaid by a series of payments each of which contains a capital portion and an interest portion. Let K be the value at rate i per annum effective of all the capital portions.

Parametric graduation may fail to achieve satisfactory results without overparameterisation. Whittaker-Henderson graduation tends to constrain the graduated values towards a low-order polynomial. Non-parametric methods do not generally make direct use of true likelihood functions. This paper suggests a method of enhancing the likelihood of a parametric graduation by means of non-parametric methods, thus reducing the disadvantages of both methods.

The parametric graduation is taken to be ideally smooth by definition and is adjusted by using constrained maximum likelihood estimation to obtain better fidelity to the experience. The constraint imposes a minimum sacrifice of smoothness, in terms of a quantitative smoothness criterion, from the initial ideal. The method is not entirely objective in that, in some cases, professional judgement is required in order to assess the degree of smoothness that can be imposed. In other cases the method provides an objective optimum. In either case, by quantifying the degrees of departure from perfect fidelity and from ideal smoothness, the suggested method provides useful and theoretically sound criteria for the purposes of the optimisation process. In particular, by inverting the parametric graduation formula for the purposes of defining the smoothness criterion, the method ensures that the smoothness criterion is consistent over the whole age range, thus resolving the main objection to non-parametric graduation.

The method is applied to the 1979-82 experience for life office pensioners in the United Kingdom with positive results.

There are few matters in connection with actuarial science of which it can be said with truth that professional knowledge has gained little during the past two decades—a period which has witnessed a remarkable expansion in both the theoretical and practical branches of the subject of life contingencies. Questions relating to extra risks, and the premiums which should be charged for them, scarcely appear, however, to have occupied the attention of actuaries to a degree at all commensurate with their commercial importance. Within the space of time alluded to above the practical side of the subject has received consideration at the hands of Mr. A. H. Bailey (J.I.A. xv, 77), and Mr. J. Meikle (J.I.A. xix, 268) ; while lines of inquiry and investigation bearing upon points of theory have been pursued by Mr. W. M. Makeham (J.I.A. xiv, 159 and 242), and Mr. J. R. Macfadyen (J.I.A. xvii, 77). Mr. A. G. Mackenzie has also contributed to our available stock of information on the subject in his Note on War Mortality, read before the Actuarial Society of Edinburgh in 1872. I venture to submit, however that there still remains much to be done to bring this branch of the main subject to the same state of enlightenment and completeness that other parts of the science have now attained. The following paper is an attempt to throw light upon a point which has hitherto escaped scientific treatment; and I entertain the hope that, in some cases of official routine, the methods proposed will be found of service.

1.1. The market in British Government stocks in many ways resembles what might be called a perfect market. In particular, very large amounts can be dealt in, dealing expenses are low, powerful statistical techniques are used to identify price anomalies, and frequent switching operations take place to exploit these anomalies. Given these features, prices of stocks will vary in a highly regular manner, and it should be possible, by the application of graduation methods, to represent the price structure in mathematical terms. If such a descriptive framework can be developed solely from the principle that prices are in equilibrium under the switching action of all participants in the market, it will provide the basis for a mathematical model that could be used for many functions of portfolio management.

This paper demonstrates workflows to incorporate text data into actuarial classification and regression tasks. The main focus is on methods employing transformer-based models. A dataset of car accident descriptions with an average length of 400 words, available in English and German, and a dataset with short property insurance claims descriptions, are used to demonstrate these techniques. The case studies tackle challenges related to a multilingual setting and long input sequences. They also show ways to interpret model output and to assess and improve model performance, by fine-tuning the models to the domain of application or to a specific prediction task. Finally, the paper provides practical approaches to handle classification tasks in situations with no or only few labelled data. The results achieved by using the language-understanding skills of off-the-shelf natural language processing (NLP) models with only minimal pre-processing and fine-tuning clearly demonstrate the power of transfer learning for practical applications.

For the past few years, stimulating research has been carried out on ordered statistics. Linear combinations of the sample ordered values are used to provide estimates of parameters of the population from which the sample is drawn. Such statistics are termed systematic by Mosteller. They are in common use, because they provide simple solutions of parametric problems of statistical estimation. Often they are inefficient, but this drawback is sometimes more than offset by the ease with which the calculations are performed.

Mosteller drew attention to the possible use of the statistics Wr , which he called quasi-range of rth order and defined as

where x 1, x 2,…, x n are ordered observations in a sample of n from a population f(x) (x 1 < x 2 < … < xn ). The distributions of quasiranges in samples drawn from a normal population have been studied by Godwin and Cadwell.