This study aims to carry out and document a systematic analysis of the literature on the importance of actuarial management in insurance managerial decision-making in the twenty-first century. After a short introduction to the business context, the paper presents an analysis of a rigorous review of the literature published between the years 2000 and 2020, which highlights the benefits and challenges of the formal application of various risk management tools. The following topics are emphasized: (i) actuarial cycle control and uncertainty management, (ii) quantitative strategic risk framework and financial modelling, and (iii) enterprise risk management with a value-based approach. This work will help future researchers to gain a better understanding of, and explicitly account for, the different contributions and benefits of actuarial management in the context of managerial decision-making in an organisation.

Presidential Addresses are an opportunity to survey the actuarial landscape, and this one is no exception. The pace of change and scope of work undertaken by actuaries since the President qualified is commented upon. Many of the current and future issues are also aired, from bonus rates and pensions mis-selling to stakeholder pensions and long-term care. Regulation, in a number of areas, is also reviewed. The regular topics of education, examinations and continuous professional development also feature.

The present paper is a continuation of that in the Companion for 1840, on the application of Barrett's method of calculating Me contingencies. No tables were then published for contingencies involving two lives; but since that time Mr. Jones's tables have appeared, in his work on the subject in the Library of Useful Knowledge. It may therefore be worth while to collect and describe the formulæ relative to two lives which are most likely to be useful in practice; with some other matters, which may partly interest the actuary and partly the commencing; student.

This paper considers five issues arising from guaranteed annuity options in pension policies issued by United Kingdom life assurance companies. These are the investment strategies for such options, the implications for bonuses on with-profits policies, the measurement of the solvency position and preparation of accounts of the companies concerned, and the policy debate on compulsory annuitisation. In particular, the paper highlights the impact of improving mortality on the value of options, comments on the House of Lords judgment in the Equitable Life case, and suggests additional disclosures in the accounts of life assurance companies.

1.1 On 21 December 1976 I received the following memorandum from Mr A. E. Tinckler, who was then the Actuary of my Company. It read:

1.2. “We have been discussing recently some of the effects on the Life Fund of a significant fall in interest rates, and I think we agree that the time has now come to set up a formal study to analyse the problem and to make recommendations.

1.3. “There is no doubt that interest rates in the United Kingdom are very much higher at the present time than in other comparable countries. There are good reasons for this state of affairs, but it is most unlikely to continue over more than a few years, unless the country is to descend to very low levels indeed in the international league. In spite of many pessimistic assertions to the contrary, there are good grounds for thinking that the present rates will come down very substantially indeed over the next few years.

Little space in the Journal has been devoted in the past specifically to graduation tests, and nowhere have the tests generally applied been concisely set out and fully discussed. The only papers during the last forty years on the subject have been by Seal and Daw; both these papers were submitted and discussed during the war years, with the result that many actuaries were unable to be present and state their views; indeed, many of us did not even know of them until the numbers of the Journal in question were published, and an opportunity to study them did not arise until after the war.

Mortality improvement has traditionally been analysed using an array of statistical methods, and extrapolated to make actuarial projections. This paper presents a forward-looking approach to longevity risk analysis which is based on stochastic modelling of the underlying causes of mortality improvement, due to changes in lifestyle, health environment, and advances in medical science. The rationale for this approach is similar to that adopted for modelling other types of dynamic insurance risk, e.g. natural catastrophes, where risk analysts construct a stochastic ensemble of events that might happen in the future, rather than rely on a retrospective analysis of the non-stationary and comparatively brief historical record.

Another feature of prospective longevity risk analysis, which is shared with catastrophe risk modelling, is the objective of capturing vulnerability data at a high resolution, to maximise the benefit of detailed modelling capability down to individual risk factor level. Already, the use by insurers of postcode data for U.K. flood risk assessment has carried over to U.K. mortality assessment. Powered by fast numerical computation and parameterised with high quality geographical data, hydrological models of flood risk have superseded the traditional statistical insurance loss models. A decade later, medically-motivated computational models of mortality risk can be expected to gain increasing prominence in longevity risk management.

When a mass of results are to be calculated and added up, it generally happens that a small fraction is of little consequence in each item, except as the little of which many make a mickle. The money calculator knows nothing of the principle that it is very hard, next to impossible, practically quite impossible, to get a mickle out of positives and negatives, when both are sure to occur in equal numbers in the long run, and with equal quantities. Generally speaking, the items of money calculations are determinable, and accuracy to the penny below the true result is a matter of contract. But in life contingencies, in which a certain amount of inaccuracy is known to lurk in the fundamental tables, no real truth is gained by tacking shillings, pence, and farthings, on to hundreds of pounds. If the nearest pound be always taken, granting that the calculated result shall be thereby a little altered, no man alive can say whether that alteration shall be approach to, or recession from, what we should call absolute truth, if our tables were perfect: it is as likely to be one as the other.

IN the preparation of this paper I met at the outset with certain difficulties.

The practice of Employers’ Liability Insurance is unfamiliar to many members of this Institute, the subject has not previously been dealt with at one of our sessional meetings, and the pages of the Journal contain very little matter bearing thereon, I fear, therefore, that if the subject is confined within the strict limits suggested by the title, the prospect of a full discussion will be jeopardized. As probably the opportunity of a discussion is the best justification for a paper on the Valuation of Employers’ Liability Contracts at the present time, I hope that the inclusion of a certain amount of introductory matter, with a view to facilitating the study of the paper, will be excused.

1.1.1. In October 1980 the Council of the Faculty of Actuaries set up a Working Party with the following brief:—

• (1) To investigate the criteria by which the solvency of life assurance companies should be assessed and to determine the amount of the solvency margin which should be required in practice by supervisory authorities. The existing requirements of the E.E.C. Life Establishment Directive should be considered with a view to recommending any desirable alterations thereto to be made when those requirements are reviewed in due course by the E.E.C. Commission. In carrying out its work the Working Party should co-operate with Working Parties or Committees of other actuarial bodies.

• (2) To report the result of their investigations to Council.

Traditional and standard discounted cash flow valuation techniques are unable to deal with a variety of options contained in lease contracts. In the United Kingdom the most important embedded option is the upward-only rent review. This becomes more valuable to the landlord in an era of low demand and low inflation, as nominal market rents are more likely to fall. Lease contracts are freely negotiated between landlord and tenant, and alternative forms of rent review clause would fundamentally change the investment characteristics of property. Many other less common options also exist in lease contracts and these create further valuation difficulties. It is essential that property valuation techniques be developed that explicitly value the options in lease contracts.

The paper is in the nature of a summary of the authors' book “Surplus in British Life Assurance—Actuarial Control over its Emergence and Distribution during 200 Years”. Copies may be purchased direct from the Institute of Actuaries (price 17s. 6d.). Members and Students of the Faculty may obtain a copy for personal use at the reduced price of 11s. post free. It begins with a survey of the principal factors that have influenced the development of theory and practice in regard to surplus throughout the years. It describes the manner in which surplus first arose in scientific life assurance, and traces how this and other historical developments have had an important effect both in the early days and later as a valid standard of equity was gradually evolved. At the same time the influence of long-dated contracts and of the expectations of the public has been a stabilising factor in spite of rapid changes in the economic and social scene.

The characteristics of the nineteenth-century image of equity are described, and the history of the twentieth century in regard to surplus is seen as one of attempts to preserve that image through sharp and contrasting vicissitudes. This idea is explored in some detail for both ordinary and industrial life business.

The problems of the present day are reviewed one by one and the paper touches on such matters as economic inflation, the public demand for pension schemes, the introduction of computers and data-processing devices and the prospect of Britain joining the Common Market. Against this background, various modern concepts of equity are contrasted and brief reference is made to matching, immunisation and gearing. Equity in with-profit pension schemes and systems of variable policies are also considered.

This general survey leads the authors in the end to ask some critical questions about the performance of the profession throughout its history. These questions relate to the success or otherwise of actuaries in foreseeing the future, in attaining equity and in progressing with the times. The authors attempt to answer them and are able to end on a cheerful note as regards past achievements and to express great hopes for the future, which may well bring a new era for the profession.

When a series of quantities which depend on a fixed law, whether known or implied, follow each other in a due order of succession, the general accuracy of their numerical values may be satisfactorily tested by observing the regularity of the progression of a suitable order of differences. If the tabular quantities are the results of calculation from a given formula, with equidistant arguments, by differencing them up to a certain order the existence of an isolated error, if one should exist, is thus prominently exhibited and therefore speedily detected. Moreover the precise locality of the error and the fact of its individuality being indicated by a characteristic interruption of the law of progression, the proper correction is ascertained by carefully noting the central position of the disturbance, and revising the corresponding portion of the original computation. This work of revision may, however, be dispensed with, if necessary or desirable, as the magnitude as well as the locality of the indicated error can in general be readily deduced, with sufficient accuracy, directly from the differences, by the method of adjustment here given. The method, being so far independent of fundamental origin, is therefore equally applicable to the adjustment of a series of quantities derived from observation, or from statistical data; only in this latter case, as almost every quantity must be more or less affected by imperfections arising from defective information and other known or unknown incidental causes, the influence of which may sometimes be augmented by paucity of numbers, the progression of the differences is disturbed by a more complicated combination of the effects of an irregular series of errors, and it becomes more difficult to eliminate the value of each separate correction.