This paper develops a multiple state model to project the number of people with disabilities in the United Kingdom over the next 35 years, thereby identifying implications for demand for long-term care for the elderly in the future.

The model requires three types of data: prevalence rate data, transition rate data and trends data. Recent trends in healthy life expectancy data are used to frame the assumptions made regarding changes in the disability rates of the U.K. population in the future.

Although there will be a large increase in the number of elderly people in the U.K. over the next 35 years, the projections suggest that the implications for the number of elderly people requiring long-term care could be ameliorated by a reduction in the proportion of older people who are severely disabled.

Late-life mortality patterns are of crucial interest to actuaries assessing longevity risk. One important explanatory variable is year of birth. We present the results of various analyses demonstrating this, including a statistical model which lends weight to the importance of year-of-birth effects in both population and insured data. We further find that a model based on age and year of birth fits United Kingdom mortality data better than a model based on age and period, suggesting that cohort effects are more significant than period effects. The financial implications of these cohort effects are considerable for portfolios with long-term longevity exposure, such as annuities written by insurance companies and defined benefit pension schemes.

We discuss classes of risk measures in terms both of their axiomatic definitions and of the economic theories of choice that they can be derived from. More specifically, expected utility theory gives rise to the exponential premium principle, proposed by Gerber (1974), Dhaene et al. (2003), whereas Yaari's (1987) dual theory of choice under risk can be viewed as the source of the distortion premium principle (Denneberg, 1990; Wang, 1996). We argue that the properties of the exponential and distortion premium principles are complementary, without either of the two performing completely satisfactorily as a risk measure. Using generalised expected utility theory (Quiggin, 1993), we derive a new risk measure, which we call the distortion-exponential principle. This risk measure satisfies the axioms of convex measures of risk, proposed by Föllmer & Shied (2002a,b), and its properties lie between those of the exponential and distortion principles, which can be obtained as special cases.

This paper proposes a simple model for studying the variability of contribution rates and fund levels, when rates of return are random. The funding methods considered are those which (1) produce an actuarial liability (AL) and a normal cost (NC), and which (2) adjust the latter by a constant fraction ‘k’ of the difference between AL and the actual fund (this discrepancy is known as the ‘unfunded liability’; for a description of actuarial cost methods the reader is referred to Trowbridge (1952), Winklevoss (1977) or Turner et al. (1984)). Thus at every valuation date

total contribution = normal cost + k × (unfunded liability).

The formula for the law of mortality which I am about to explain and apply to a practical case, is not a merely empirical formula. but is based on a presumed property of the causes of death. The value of the formula is however a question which is in a great measure independent of the correctness of my hypothesis; for it is well known that even a false hypothesis may be of great service. While I shall certainly be very much interested to learn the opinion entertained by actuaries as to the theoretical part of the subject, yet the practical application of the formula is the point to which I attach most importance, and to which I would by preference invite criticism.

The appended notes, based upon the population statistics of England and Wales, fall naturally, as their title suggests, into two sections. The first consists of an attempt to identify and to measure, so far as may be possible, the more important errors introduced into the successive records through the misstatements of age to which the general population has been addicted ever since its returns were collected, and may be considered a necessary preliminary to the second, which reviews briefly the mortality experienced by that population, noting certain features in the changes which have occurred in the past and making some suggestions with regard to its possible course in the future.

In this paper we consider reserving and pricing methodologies for a pensions-type contract with a simple form of guaranteed annuity option. We consider only unit-linked contracts, but our methodologies and, to some extent, our numerical results would apply also to with-profits contracts.

The Report of the Annuity Guarantees Working Party (Bolton et al., 1997), presented the results of a very interesting survey, as at the end of 1996, of life assurance companies offering guaranteed annuity options. There was no consensus at that time among the companies on how to reserve for such options. The Report discussed several approaches to reserving, but concluded that it was unable to recommend a single approach. This paper is an attempt to fill that gap.

We investigate two approaches to reserving and pricing. In the first sections of the paper we consider quantile, and conditional tail expectation, reserves. The methodology we adopt here is very close to that proposed by the Maturity Guarantees Working Party in its Report to the profession (Ford et al., 1980). We show how these policies could have been reserved for in 1985, and what would have been the outcome of using the proposed method.

In a later section we consider the feasibility of using option pricing methodology to dynamically hedge a guaranteed annuity option. It is shown that this is possible within the context of the model we propose, but we submit that, in practical terms, dynamic hedging is not a complete solution to the problem since suitable tradeable assets do not in practice exist.

Finally, we describe several enhancements to our models and methodology, which would make them even more realistic, though generally they would have the effect of increasing the required contingency reserves

In this paper, we identify the economic system in which occupational pension schemes operate. This system includes all parties to the pension arrangement, particularly the members of the scheme and the shareholders of the sponsoring company. This requires us to model the pension scheme not as a self-contained fund, but simultaneously alongside the company, and to recognise its interaction with other parties with financial interests in the scheme. Under this method, the stakes of the various parties aggregate to 100% of the assets of the company including the assets of the pension scheme. The power of this approach is that decisions taken in relation to the management of the pension scheme can be assessed by the effect they have on the way in which the overall economic value of the company is divided between stakeholders.

In a recent paper, Kremer (1982) has shown how the classical chain ladder method for estimating outstanding claims on general insurance business is strongly related to a two-way analysis of variance. It can be argued that the estimation methods in a standard chain ladder analysis are inefficient from a statistical viewpoint and that an analysis of variance is more appropriate. Once the chain ladder method is identified with a standard statistical method, the well-known statistical theory can be used to the advantage of the claims reserver. For a further discussion of the use of main stream statistical theory applied to the least squares estimation of the linear model which is close to the chain ladder method, the reader is referred to Renshaw (1989).

The prediction of outstanding claims amounts in non-life insurance is, by its very nature, highly speculative. Partially because of this and partially because of the variety of features suggested by various researchers for possible inclusion in the structure of the underlying prediction model, the past two decades have seen a proliferation of methodologies for making such predictions. Specific details of these developments are contained in a comprehensive and highly detailed survey conducted by Taylor (1986) in which a taxonomy of methods is established. One feature common to all of these methods is the utilization of current and past records of claims amounts—invariably in the form of the familiar so-called runoff triangle or a variant thereof—to calibrate the proposed prediction model before use. Prudence dictates that diagnostic checks should then be made to establish whether or not the data are supportive of the structure imparted to the prediction model before use, a feature which apart from some notable exceptions including Zehnwirth (1985) and Taylor (1983), is not always emphasized in the literature.

Data from insurance portfolios and pension schemes lend themselves particularly well to the application of survival models. In addition to the traditional actuarial risk-rating factors of age, gender and policy size, we find that using geodemographic models based on postcode provides a major boost in explaining risk variation. Geodemographic models can be better than models based on pension size in explaining socio-economic variation, but a model using both is usually better still. Models acknowledging heterogeneity tend to fit better than models which do not. Finally, bootstrapping techniques can be used to test the financial applicability of a model, while weighting the model fit can be used to address concentration risk.

Dynamic financial analysis has become one of the important tools that actuaries use to model the underwriting and investment operations of insurance companies. The first step in carrying out the analysis is to investigate the most important factors affecting company performance. This paper identifies the determinants of the performance of United Kingdom general insurance companies using a panel data set consisting of economic data and Financial Services Authority/Department of Trade and Industry returns over the period 1986 to 1999. Three performance measures are used to capture different aspects of insurance operations. These measures are related to a number of economic and firm specific variables, chosen on the basis of relevant theory and literature. An ordinary least squares regression model and two panel data models are estimated for each of three performance measures. This paper also addresses several important econometric problems that are usually ignored in applied work in the context of panel data analysis. Based on the empirical results, this study finds that liquidity, unexpected inflation, interest rate level and underwriting profits are statistically significant determinants of the performance of U.K. general insurers.

The paper addresses the problem of estimating future claim payments from the ‘run-off’ of past claim payments. A model of the claim payment process is postulated. Results from risk theory are applied to give a model for the incremental paid claims data by development period. A fitting method is developed which takes account of the error structure of the data implied by the underlying model of the claim payment process. The application of a similar method to incremental incurred data is considered. A numerical example is given.

1.1. The purpose of this paper is to survey some new results concerning the term structure of interest rates and discuss actuarial applications. The term structure of interest rates exhibits the relationship among the yields on default free debt instruments of different maturities. Although there is a considerable volume of literature dealing with the determinants of the term structure the analysis has until recently been presented for the most part in a deterministic (i.e. non-stochastic) framework. This constrasts with the treatment of capital assets where equilibrium prices have been obtained under the assumption that returns on these assets are random variables.

This paper is concerned with the current and future financing of long-term care (LTC). This is defined as the provision of nursing and care services to those adults who are incapable, to some degree, of looking after themselves, but excluding short-term convalescent care. The current position is summarised, covering the demand and supply of LTC, how it is currently financed, new developments and consumer attitudes. The paper then goes on to consider future developments. Possible patterns of future demand, covering likely needs and costs are given. Consideration is then given as to how future demand may be financed.

The paper discusses some of the initiatives that might be undertaken to encourage proper planning by both the State and individuals and concludes that the actuarial profession should have a significant role to play in communicating the issues and evaluating solutions.

This paper updates Living with Mortality published in 2006. It describes how the longevity risk transfer market has developed over the intervening period, and, in particular, how insurance-based solutions – buy-outs, buy-ins and longevity insurance – have triumphed over capital markets solutions that were expected to dominate at the time. Some capital markets solutions – longevity-spread bonds, longevity swaps, q-forwards and tail-risk protection – have come to market, but the volume of business has been disappointingly low. The reason for this is that when market participants compare the index-based solutions of the capital markets with the customised solutions of insurance companies in terms of basis risk, credit risk, regulatory capital, collateral and liquidity, the former perform on balance less favourably despite a lower potential cost. We discuss the importance of stochastic mortality models for forecasting future longevity and examine some applications of these models, e.g. determining the longevity risk premium and estimating regulatory capital relief. The longevity risk transfer market is now beginning to recognise that there is insufficient capacity in the insurance and reinsurance industries to deal fully with demand and new solutions for attracting capital markets investors are now being examined – such as longevity-linked securities and reinsurance sidecars.