Continuing increases in life expectancy beyond previously-held limits have brought to the fore the critical importance of mortality forecasting. Significant developments in mortality forecasting since 1980 are reviewed under three broad approaches: expectation, extrapolation and explanation. Expectation is not generally a good basis for mortality forecasting, as it is subjective; expert expectations are invariably conservative. Explanation is restricted to certain causes of death with known determinants. Decomposition by cause of death poses problems associated with the lack of independence among causes and data difficulties. Most developments have been in extrapolative forecasting, and make use of statistical methods rather than models developed primarily for age-specific graduation. Methods using two-factor models (age-period or age-cohort) have been most successful. The two-factor Lee–Carter method, and, in particular, its variants, have been successful in terms of accuracy, while recent advances have improved the estimation of forecast uncertainty. Regression-based (GLM) methods have been less successful, due to nonlinearities in time. Three-factor methods are more recent; the Lee–Carter age-period-cohort model appears promising. Specialised software has been developed and made available. Research needs include further comparative evaluations of methods in terms of the accuracy of the point forecast and its uncertainty, encompassing a wide range of mortality situations.

We construct a stochastic model of an individual's lifetime that includes diagnosis with ischaemic heart disease and stroke and also the development of the major risk factors for these conditions: hypercholesterolaemia, hypertension, diabetes and obesity. Smoking, another major risk factor, is treated deterministically. Mathematically, the model is a continuous time, finite state space Markov process, with the individual's age playing the rôle of time. The model is parameterised using data from the Framingham Heart Study, with parameter values adjusted so that the model is appropriate for UK conditions in the early 21st century. The model has been designed so that it can be used to quantify the effects of:

(i) trends, in particular increasing prevalence of obesity.

(ii) changes in behaviour, in particular smoking patterns, and

(iii) treatments, in particular statins for hypercholesterolaemia.

These applications are covered in two accompanying papers.

This is the second in a series of three papers. In the first paper we describe a comprehensive stochastic model of an individual's lifetime that includes diagnosis with ischaemic heart disease and stroke and also the development of the major risk factors for these conditions. The third paper is devoted to some applications of this model.

In this paper we discuss the effect of BMI on diabetes, heart disease and mortality and we use data from the Framingham Heart Study and the Health Survey for England to develop stochastic models for changes in an individual's BMI. Some of these models incorporate time trends leading to increasing prevalence of obesity. We then use these models to investigate how future expected lifetime and future expected healthy lifetime depend on BMI.

Our conclusions are that if the prevalence of obesity increases, even to an extreme degree, then the prevalence of diabetes and hypertension in the population will increase, possibly to a significant extent, but the prevalence of heart disease and stroke will increase by a much smaller amount and the effect on expected future lifetime will be small.

This is the third in a series of three papers. In the first paper we describe a comprehensive stochastic model of an individual's lifetime that includes diagnosis with ischaemic heart disease and stroke and also the development of the major risk factors for these conditions. The second paper discusses in some detail models for changes in body mass index (BMI) and also the effects of these changes, in particular the current trend towards increasing prevalence of obesity, on diabetes, cardiovascular diseases and expected future lifetime. This paper is devoted to the following applications of the model described in the first paper:

(a) quantifying the effects of smoking and of changes in smoking habits, and,

(b) quantifying the effects of treatment with statins (drugs designed to lower cholesterol).

Høgh, Linton and Nielsen (2006) showed that the famous result in the award winning paper of Froot and Stein (1998) is not correct in the sense that their result does not follow from their assumptions. In this paper we show that the economic intuition behind the paper of Froot and Stein (1998) is correct and that their result can be obtained when the market is reformulated in a continuous time setting and modern market theory is employed.

Among the systems in place in different countries for the protection of the population against the long-term contingencies of old-age (or retirement), disability and death (or survivorship), defined-benefit social security pension schemes, i.e. social insurance pension schemes, by far predominate, despite the recent trend towards defined-contribution arrangements in social security reforms. Actuarial valuations of these schemes, unlike other branches of insurance, continue to be carried out almost exclusively on traditional, deterministic lines. Stochastic applications in this area, which have been restricted mainly to occasional special studies, have relied on the simulation technique. This paper develops an analytical model for the stochastic actuarial valuation of a social insurance pension scheme. Formulae are developed for the expected values, variances and covariances of and among the benefit expenditure and salary bill projections and their discounted values, allowing for stochastic variation in three key input factors, i.e., mortality, new entrant intake, and interest (net of salary escalation). Each deterministic output of the valuation is thus supplemented with a confidence interval, that is, a range with an attached probability. The treatment covers the premiums under the different possible financial systems for these schemes, which differ from the funding methods of private pensions, as well as the testing of the level of the Fund ratio when the future contributions schedule is pre-determined. Although it is based on a relatively simplified approach and refers only to retirement pensions, with full adjustment in line with salary escalation, the paper brings out the stochastic features of pension scheme projections and illustrates a comprehensive stochastic valuation. It is hoped that the paper will stimulate interest in further research, both of a theoretical and a practical nature, and lead to progressively increasing recourse to stochastic methods in social insurance pension scheme valuations.

The impact that asset allocation has on the economic capital and the risk adjusted performance of financial services firms is considered in this article. A stochastic modelling approach is used in conjunction with a life insurance annuity firm illustrative example. It is shown that traditional solvency driven deterministic approaches to financial services firm asset allocation can yield sub optimal results in terms of minimising economic capital or maximising risk adjusted performance. Our results challenge the conventional wisdom that the assets backing life insurance annuities and financial services firm capital should be invested in low risk, bond type, assets. Implications for firms, customers, capital providers and regulators are discussed.

This paper examines various forms of individual claim model for the purpose of loss reserving, with emphasis on the prediction error associated with the reserve. Each form of model is calibrated against a single extensive data set, and then used to generate a forecast of loss reserve and an estimate of its prediction error.

The basis of this is a model of the “paids” type, in which the sizes of strictly positive individual finalised claims are expressed in terms of a small number of covariates, most of which are in some way functions of time. Such models can be found in the literature.

The purpose of the current paper is to extend these to individual claim “incurreds” models. These are constructed by the inclusion of case estimates in the model's conditioning information. This form of model is found to involve rather more complexity in its structure.

For the particular data set considered here, this did not yield any direct improvement in prediction error. However, a blending of the paids and incurreds models did so.