Gompertz's Function for expressing the probability of a person surviving anygiven period, x, is . For thepurpose of adapting this expression to the entire period of adult life Ihave added the factor ∈−ax. The two expressionsbecome identical in form when the factor∈−δx representing the effect of discount is introduced, and both may therefore becorrectly designated by the name of “Gompertz's Function.”

This paper puts the case for the Actuarial Profession revising and tightening its standards on actuarial funding advice in relation to United Kingdom occupational pension schemes. We critique current actuarial practice and advocate principles for measuring solvency and providing funding advice. In particular, we advocate that funding targets should be clearly and unambiguously related to scheme solvency. The paper also covers optimal investment strategy, treatment of the ‘company covenant’ when giving funding advice and governance issues relating to pension schemes.

1. This paper originated with a sense of irritation at the way in which the graduation of age rates of mortality has become more and more complicated by the apparent determination to assume some underlying law of mortality, a law which could not possibly be deduced from observations in the past or present man-made conditions of dangerous living. It then developed into a consideration of graduation from a less frequently adopted point of view, i.e. a look at the distribution of lengths of life (the so-called curve of deaths). This led inevitably to a review of the long-pursued controversy as to whether or not there is a predetermined biological maximum to the human lifespan under ideal conditions and beyond that to a review of the biological evidence for this maximum and the possibility of extension by environmental or medical intervention. Finally, this led to the likely results of such environmental and medical advances and to some experiments in mortality projection.

In this paper a system for recommending investment channel choices to members of defined contribution retirement funds is proposed. The system is interactive, using a member's answers to a series of questions to derive a utility function. The observed values are interpolated by means of appropriate formulae to produce a smooth utility function over the whole positive range of benefits at retirement. The resulting function, together with stochastic models of the returns on the available channels and of the annuity factor at exit, is then used to recommend an optimum apportionment of the member's investment. The proposed system is applied to the observed values of utility functions of post-retirement income elicited from members of retirement funds. Difficulties in the application are discussed and the results are analysed. The sensitivity of the recommendations to the parameters of the stochastic model is discussed.

The Management Board of the UK Actuarial Profession has identified enterprise risk management (ERM) as an area of growth, particularly within the financial sector. It is an area which offers opportunities for actuaries, working with other disciplines, to move out of their traditional sectors of employment, with the skill set required fitting well with an actuary's training and practical focus.

Members of the Profession also highlighted ERM as one of the two main areas where they wanted the Profession to focus their research efforts in the membership survey in 2009. Consequentially the Management Board allocated funds to support research projects in ERM in 2010–2011 and has worked with the ERM Practice Area Committee to identify the topics that they feel most suited to external research where the outputs will have a broad strategic value to the financial services sector.

The focus of the paper is non-profit lifetime annuities in the UK. Annuity insurers have been faced with, or have initiated, an unprecedented amount of change during the last decade, and rapid change is still continuing. We draw out implications for the actuarial management of the business, arising from the evolution of: longevity risk assessment and management, investment strategy and operations, financial reporting, and enterprise risk management. We discuss Solvency II in some technical depth, analysing the proposed rules for technical provisions and solvency capital requirement.

1. These notes were written after Scott's Faculty paper “A Reserve Basis for Maturity Guarantees in Unit-Linked Life Assurance”, discussed on 17th January 1977, but before Corby's Institute note “Reserves for Maturity Guarantees Under Unit-Linked Policies”, discussed on 28th March 1977; they are a kind of extended written contribution to the first paper.

Deep neural network models have substantial advantages over traditional and machine learning methods that make this class of models particularly promising for adoption by actuaries. Nonetheless, several important aspects of these models have not yet been studied in detail in the actuarial literature: the effect of hyperparameter choice on the accuracy and stability of network predictions, methods for producing uncertainty estimates and the design of deep learning models for explainability. To allow actuaries to incorporate deep learning safely into their toolkits, we review these areas in the context of a deep neural network for forecasting mortality rates.

In 1970 the Association Royale des Actuaires Belges celebrated the 75th anniversary of its foundation. To mark the occasion, the Association had in the previous year invited papers to be submitted on two subjects, one of which was ‘Determination of the heterogeneity of the classes of risks’, and the paper which follows this introductory note was one of those submitted on this subject. The paper deals exclusively with motor insurance, in which the study of heterogeneity must be regarded as being of major importance, and discusses both the measurement of heterogeneity and the relationship between heterogeneity and methods of experience rating such as the no claim discount (NCD) systems used in the United Kingdom.

1.1 In March 1987 the Futures Committee of the Institute considered a preliminary report (Daykin, 1987) on the possible impact of AIDS in the United Kingdom and the consequences for life insurance. The Committee recommended the setting up of a Working Party to study the problem. The Working Party on AIDS was accordingly established, under the auspices of the Research Committee. The authors of this paper formed the membership of the Working Party, under the chairmanship of C. D. Daykin.

The development of sickness insurance of the type dealt with in this paper has been a long process, commencing in a tentative fashion, probably a century ago, in Europe. In 1900, E. Hamza, at that time actuary of a Russian insurance company, contributed to the Third International Congress a paper of interesting historical significance which is clearly based on long experience in Germany. In his paper he developed an approach fundamentally different from the traditional British approach. British methods—which can be described with complete adequacy at this stage as a continuation of Friendly Society actuarial technique—have stood the test of time for at least 150 years and it is the purpose of this paper to analyse the two lines of development; to pose the question of their efficacy in the future; and to outline alternative methods depending on modern mathematical techniques.

The Decennial Supplement on Occupational Mortality published in 1978 commented on mortality differences between the social classes (Chapter 8) using data from the 1971 Census and the deaths in the period 1970–72. The analysis was based on life tables prepared for the individual social classes from which derived indices, for example expectations of life, were calculated. It is proposed here to repeat this exercise using the data for males recently published in microfiche form by the Office of Population Censuses and Surveys—OPCS. This time, the Decennial Supplement has omitted to provide an analysis and commentary and we propose to make some attempt to remedy this deficiency. In our analysis, the Decennial Supplement data have been supplemented by data from the OPCS Longitudinal Study.

For life insurers in the United Kingdom (UK), the risk margin is one of the most controversial aspects of the Solvency II regime which came into force in 2016.

The risk margin is the difference between the technical provisions and the best estimate liabilities. The technical provisions are intended to be market-consistent, and so are defined as the amount required to be paid to transfer the business to another undertaking. In practice, the technical provisions cannot be directly calculated, and so the risk margin must be determined using a proxy method; the method chosen for Solvency II is known as the cost-of-capital method.

Following the implementation of Solvency II, the risk margin came under considerable criticism for being too large and too sensitive to interest rate movements. These criticisms are particularly valid for annuity business in the UK – such business is of great significance to the system for retirement provision. A further criticism is that mitigation of the impact of the risk margin has led to an increase in reinsurance of longevity risks, particularly to overseas reinsurers.

This criticism has led to political interest, and the risk margin was a major element of the Treasury Committee inquiry into EU Insurance Regulation.

The working party was set up in response to this criticism. Our brief is to consider both the overall purpose of the risk margin for life insurers and solutions to the current problems, having regard to the possibility of post-Brexit flexibility.

We have concluded that a risk margin in some form is necessary, although its size depends on the level of security desired, and so is primarily a political question.

We have reviewed possible alternatives to the current risk margin, both within the existing cost-of-capital methodology and considering a wide range of alternatives.

We believe that requirements for the risk margin will depend on future circumstances, in particular relating to Brexit, and we have identified a number of possible changes to methodology which should be considered, depending on circumstances.

A Former President of the Institute once remarked that whereas the graduation of a mortality table might be considered a specialized technique not required by the practising actuary, the efficient testing of any graduation submitted to him should be an integral part of his actuarial ability. The student anxious to equip himself in this respect encounters considerable divergence of opinion regarding the best method of testing a graduation. There is complete agreement as to the duality of purpose of such a test: smoothness and fidelity to the data are essential factors. But whilst the criterion of smoothness is easily formulated—the run of the second or third differences of qx must show no awkward breaks—the views relating to the tests of adherence to the data are divided between the application of a “mean deviation” rule at each age or group of ages and a purely “practical” judgment based on that elusive virtue, experience.

A first order autoregressive model was proposed in Wilkie (1995) for the retail price inflation series as a part of his stochastic investment model. In this paper we apply time series outlier analysis to the data set and a revised model is derived. It significantly alleviates the problem of leptokurtic and positive skewed residual distribution as found in the original model. Finally, ARCH models for the original series and the outlier-adjusted data are also considered.

The paper traces the history of the development of a with-profit system for a specialist unit-linked office. The marketing problem, to which this was the chosen solution, is discussed and a number of possible future developments are then considered. The second half of the paper is devoted to discussion of the question of matching assets and liabilities for the range of products developed. Although the paper deals with developments in a particular office the authors' intention is to provide a different perspective on the problems associated with conventional with-profit business which will be of more general interest.

This paper considers the application of discounted cash flow (DCF) techniques to the analysis of the property investment market. The traditional method of property valuation is briefly outlined and its shortcomings highlighted. An alternative DCF procedure is derived to calculate the present value of a property investment. This method will be familiar to actuaries, but is not always used in property disciplines. The sensitivities of this formulation to changes in the force of real interest, force of real rental growth and force of inflation are derived. It is suggested how these formulae may be used for property investment appraisal and risk analysis. We conclude that DCF offers a more flexible and accurate means of estimating the value of a property, and that property valuers, financial economists and actuaries should work jointly to develop practical DCF methods. However, so long as traditional methods of valuation prevail, a rational investor must use both methods to identify mispriced property assets. There have been few property contributions to the actuarial literature in the United Kingdom; this paper is intended to build on the few previous papers and suggests directions for future work.

A Dread Disease contract pays out a lump sum on the diagnosis of any of a number of specified diseases. Those most commonly covered are heart attack, coronary artery disease requiring surgery, cancer and stroke. The benefit can take either of two main forms—it may provide an acceleration of all or part of any death benefit or it may be an additional benefit. It can be sold in conjunction with many conventional products or as a stand-alone policy.

Dread Disease contracts were originally developed in South Africa in the early 1980's, although cancer riders had previously been sold in the U.S.A., Japan and Israel. To some extent the marketing of these contracts was insensitive and preyed on people's fears in a distasteful way. This may explain some initial reluctance amongst U.K. insurers to enter this market; however with marketing literature now emphasizing more positive aspects, this appears to have been overcome.