The volumes of the Journal contain numerous theoretical investigations dealing with the changes produced in Policy-values by alterations in the basis of valuation, and a number of interesting and important results have been obtained, of which the most valuable have been embodied in the Text-Book, Part II, Chapter xviii, Articles 39–72. These investigations are almost entirely based upon analytical transformations of algebraical expressions for the Policy-value. Fruitful as this method has been, and elegant as are many of its processes and results, it yet labours under certain serious disadvantages. From the nature of the method it can be applied only to the limited class of benefits—practically confined to ordinary Whole-Life and Endowment Assurances, with uniform Premiums and Benefits—which admit of the Policy-values being expressed in an algebraical form involving only one class of function, e.g., ax, Ax or Px: so that relations which are really of very wide generality remain undemonstrated, except for those particular classes of Assurance. Again, demonstrations based upon a particular mathematical formula for the Policy-value are not easily modified to meet changes of conditions which, though slight in themselves, may render the fundamental formula completely inapplicable: while abstract analytical demonstrations are both harder to grasp in the first instance, and harder to reproduce or adapt when subsequently required, than are demonstrations based upon more concrete considerations.

In considering the various methods of graduation open to us, we were impressed, having regard to the large number of series to be dealt with, by the great facility and rapidity with which formulæ of summation can be applied with the certainty that the results obtained will conform closely to the unadjusted facts. For the Sickness Tables the summation method is especially suitable, since the average number of weeks (or rate) of sickness at any age is necessarily separable for practical purposes into “periods of attack”, e.g., in the case of the Manchester Unity Experience, 1893–97, “First 3 Months”, “Second 3 Months”, “Second 6 Months”, “Second 12 Months,” and “After 2 years”, the successive values of each of which must form a regular series, whilst the sum of any two sections forming a “period of attack” in general use (e.g., First 6 Months = First 3 Months + Second 3 Months) must be equally regular in progression. It is obvious that if a summation method be adopted, and the same formula be used throughout, a combination of any two or more of the graduated series will be itself a graduated series, and will, indeed, be identical with the result of an independent graduation of the combined unadjusted rates.

A FIMAG Working Party was set up in 1989 to consider the stochastic investment model proposed by A. D. Wilkie, which had been used by a number of actuaries for various purposes, but had not itself been discussed at the Institute. This is the Report of that Working Party. First, the Wilkie model is described. Then the model is reviewed, and alternative types of model are discussed. Possible applications of the model are considered, and the important question of ‘actuarial judgement’ is introduced. Finally the Report looks at possible future developments. In appendices, Clarkson describes a specific alternative model for inflation, and Wilkie describes some experiments with ARCH models. In further appendices possible applications of stochastic investment models to pension funds, to life assurance and to investment management are discussed.

Investment efficiency is a function of the risk, return and total cost of an investment management structure, subject to the fiduciary and other constraints within which investors must operate. Institutional investors implement their investment policies through investment management structures. In this paper the aim is to enhance the investment management structure by broadening the financial objectives, by recognising the effect of behavioural issues and by incorporating governance constraints. We therefore suggest that investment efficiency should be considered as a combination of financial efficiency and non-financial efficiency.

Modern portfolio theory had a revolutionary effect on portfolio construction. In the same way, we believe that investment management structures should be constructed in a more disciplined and quantitative manner. In this paper we outline the quantitative and qualitative methods by which these structures can be developed. The proposed new framework for designing investment management structures seeks to optimise net information ratios while simultaneously recognising the level of regret risk facing fiduciaries, minimising non-financially-productive behavioural biases and taking account of the resources available to the fiduciary to monitor these structures.

One of the highlights of the year 1613 was the burning down of the Globe Theatre in London, during a performance of Shakespeare's newly-written ‘Henry VIII’, when the discharge of a piece of ordnance set fire to the thatch.

Another event which took place during the year was less spectacular but, to actuaries, just as noteworthy. This was the publication of a book by Richard Witt entitled: Arithmeticall Questions, touching The Buying or Exchange of Annuities; Taking of Leases for Fines, or yearly Rent; Purchase of Fee-Simples; Dealing for present or future Possessions; and other Bargaines and Accounts, wherein allowance for disbursing or forebeareance of money is intended; Briefly resolved, by means of certain Breviats. (See Title Page in Figure 1 on facing page).

We investigate the link between death rates and smoking prevalence in ten developed countries with the aim of using smoking prevalence data to explain differences in country-specific death rates. A particular problem in building a stochastic mortality model based on smoking prevalence is that there are in general no separate mortality data for smokers and non-smokers available. We show how we can estimate mortality rates for smokers and non-smokers using information about the smoking prevalence in a number of developed countries, and making an additional assumption about the death rates of smokers. We consider this empirical investigation to be the first step towards a consistent mortality model for multiple populations, which will require modelling of country specific differences in mortality, as well as non-smokers’ and smokers’ mortality rates.

The distribution of insurance claims in a given time period is usually regarded as a random sum. This paper sets up a time series model for the value of the claims and combines it with a model for the number of claims. Thus past observations can be used to make predictions of future values of the random sum, and the overall model ensures that they are discounted appropriately. It is shown that explanatory variables can be introduced into the model, and how it can be extended to handle several groups. The general approach is based on the recently developed structural time series methodology.

This paper considers cross-validation as an objective and risk-based method for selecting the smoothing parameter in a non-parametric graduation. In addition, the relative merits of two kernel estimators are compared in the context of mortality graduation. Finally, it is well known in the statistical literature that the use of theoretically superior kernels is not as important as the choice of bandwidth. Our results support this conclusion, suggesting that the focus on such weights is misguided in the actuarial textbooks on moving weighted averages.

The current banking crisis has reminded us of how risks materialising in one part of the financial system can have a widespread impact, affecting other financial markets and institutions and the broader economy. This paper, prepared on behalf of the Actuarial Profession, examines how such events have an impact on the entire financial system and explores whether such disturbances may arise within the insurance and pensions sectors as well as within banking. The paper seeks to provide an overview of a number of banking and other financial crises which have occurred in the past, illustrated by four case studies. It discusses what constitutes a systemic event and what distinguishes it from a large aggregate system wide shock. Finally, it discusses how policy-makers can respond to the risk of such systemic financial failures.

8.1 This paper is concerned with the selection of investment portfolios to meet specified criteria which involve the liabilities of a long term investing institution such as a pension fund or a life office. In Part 1 (5) I showed a certain relationship between, on the one hand, portfolios selected according to a criterion of pure matching to the liabilities and, on the other hand, portfolios selected according to a more general criterion of ‘efficiency’. This connection points to a particular actuarial approach to the selection of portfolios, which is now further examined in Part 2.

8.2 Writing Part 2 separately presents an opportunity to re-state the main ideas. The next few paragraphs recapitulate the basic points with a view to reducing, within the subsequent discussion, the amount of cross-reference to Part 1, and to the three preceding papers on which the study is based.

Much actuarial work is underpinned by the use of economic models derived from mainstream academic theories of finance and economics which treat money as being a neutral medium of exchange. The sustainability of a financial system whose understanding is based on a limited view of the role of money has increasingly been subject to criticism. In order to identify needed research programmes to address such criticisms and improve these disciplines, we sought to understand the current state of knowledge in economics and finance concerning the link between monetary and financial factors and sustainability. We have approached this through a search for relevant literature published in the highest-rated academic journals in economics, finance and the social sciences for titles and abstracts containing both references to the financial system on the one hand, and sustainability and environmental factors on the other. The systematic search of a universe of 125 journals and 355,000 articles yielded the finding that surprisingly few research papers jointly address these concepts. Nevertheless, we find that current research shares a broad consensus that the implications of the growth-oriented economic model results in an increasingly interconnected and fragile financial system whose participants are not incentivised to fully recognise the natural environment and resource constraints. We further observe that the prescriptions offered are relatively limited and small-scale in their outlook and that there is a vital need for further research, particularly for actuaries who are required to take a longer-term outlook. The Resource and Environment Board has supported this work with two key objectives: first, to identify research that may have direct application to actuarial work and, second, to identify gaps in academic research that would help drive the Institute and Faculty of Actuaries’ own research agenda. With this in mind there are three further areas of potential actuarial research. These are the policy aim of pursuing growth without limit within a finite ecosystem; discount factors as the primary means of capital allocation and investment decisions; and the use of gross domestic product as the key metric of economic activity and success. We also conclude that further academic research is urgently needed to understand the sustainability of the banking and monetary system.

This paper discusses the use of parametric models for description of the term structure of interest rates and their uses. We extend earlier work of Cairns (1998), Chaplin (1998) and Feldman et al. (1998), by presenting new theoretical results and also by demonstrating that the same model can be applied to countries other than the United Kingdom. First, we prove that the process of fitting a yield curve to price data has a unique optimal solution in both zero-coupon-bond and low-coupon-bond markets. Furthermore, an alternative method of curve fitting to those proposed previously is shown to have a unique solution in all markets.

The restricted-exponential model has previously been applied to U.K. data (Cairns, 1998). Here, we consider its wider application in European bond markets. In particular, we analyse German market data and conclude that the same model applies equally well to both countries.

Assessing longevity risk is crucial to the financial management of annuities and longevity-related financial instruments. Actuaries have been using socio-economic circumstances (SEC) of individuals estimated through postcodes, pension size and occupation to price annuities for prospective customers. Differences in mortality rates of people in different SEC have been discussed extensively but less is known about how their mortality rates have changed over time.

A lack of regular, consistent and credible mortality data for people in different SEC has hampered the study of historical mortality trends. This in turn has made forecasting a greater challenge. To address some of these data issues, we have obtained mortality and population data between 1981 and 2007 for England, divided into SEC quintiles (measured by the relative deprivation of the area of residence according to the Index of Multiple Deprivation (IMD) 2007). Using the data, we have analysed the mortality trends by SEC. These findings can provide insight into mortality improvement for people in different SEC. This can contribute to commercial decisions for annuity businesses, reinsurance and longevity swaps.

This paper covers a number of different topics related to the measurement and modelling of dependency within economic capital models. The scope of the paper is relatively wide. We address in some detail the different approaches to modelling dependencies ranging from the more common variance-covariance matrix approach, to the consideration of the use of copulas and the more sophisticated causal models that feature feedback loops and other systems design ideas.

There are many data and model uncertainties in modelling dependency and so we have also endeavoured to cover topics such as spurious relationships and wrong-way risk to highlight some of the uncertainties involved.

With the advent of the internal model approval process under Solvency II, senior management needs to have a greater understanding of dependency methodology. We have devoted a section of this paper to a discussion of possible different ways to communicate the results of modelling to the board, senior management and other interested parties within an insurance company.

We have endeavoured throughout this paper to include as many numerical examples as possible to help in the understanding of the key points, including our discussion of model parameterisation and the communication to an insurance executive of the impact of dependency on economic capital modelling results.

The economic capital model can be seen as a combination of two key components: the marginal risk distribution of each risk and the aggregation methodology which combines these into a single aggregate distribution or capital number. This paper is concerned with the aggregation part, the methods and assumptions employed and the issues arising, and not the determination of the marginal risk distributions which is equally of importance and in many cases equally as complex.

When I was invited to read this paper I felt not only honoured but particularly pleased to be given the opportunity to set forth for your criticism the views I have come to hold concerning the complex of problems centred round the use of Bayes's theorem. For what body of people has for longer been engaged in the application of the mathematical doctrine of probabilities to the affairs of life? And so, what body could be better fitted to judge the merits and the faults of any attempt to clarify the principles of the subject? It is no accident that the original publication of Bayes's famous paper was brought about by the author of the Northampton Life Table; and in the modern period, in dealing with the criticisms of Bayes's postulate stemming from Boole, the credit for a major advance is shared between Sir Harold Jeffreys and Mr Wilfred Perks, independent originators of the theory of invariant prior distributions. And, to anticipate a point I shall develop in more detail later on, it appears to me that the experience of actuaries in the formation of categories as, for instance, by occupational group, as abstainers or non-abstainers, and so on, can be highly relevant to the effective use of Bayes's theorem in many wider contexts; and an examination of the principles underlying the formation of categories should improve our insight into problems of statistical inference in general.

In an earlier introductory paper (J.I.A.107, 513), Balzer and Benjamin (1980) presented a model of an insurance system with delayed profit/loss sharing feedback from insurer to insured. The system was considered from a general control and dynamic systems theory viewpoint. Certain fundamental concepts were introduced and the dynamic responses of cash flow f(k) and accumulated cash flow fa(k) to an isolated group of unpredicted claims presented. This paper takes the analysis further in a number of important ways.

The general structure and details of the mode1 of the insurance system can be found in the earlier paper.

This paper addresses one of the fundamental issues faced by offices in the transacting of with-profits business, namely, the provision of equity-related performance along with maturity guarantees that increase over the lifetime of the policy. The approach commonly followed of using capital to cover the office's investment mismatch risk is considered from an individual policy viewpoint, and, through stochastic modelling, the degree of security represented by different reserve levels identified. An alternative approach using derivatives to provide similar levels of security is then presented and the range of policy proceeds resulting from the two methods compared. While it is recognised that the latter approach may have limited application in practice, the ideas presented could form the basis of a new approach to pricing guarantees under with-profits business that would be consistent with the pricing of current derivative-backed guaranteed products.

The purpose of this paper is to describe a methodology for determining an appropriate structure for time-series models of inflation rates, short-term and long-term interest rates, dividend growth rates, dividend yields, rental growth rates and rental yields and to demonstrate the application of that methodology to the development of a model based on South African data. It is suggested that the methodology used in this paper may be applied to other economic environments.