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The relative merits of different parametric models for making life expectancy and annuity value predictions at both pensioner and adult ages are investigated. This study builds on current published research and considers recent model enhancements and the extent to which these enhancements address the deficiencies that have been identified of some of the models. The England & Wales male mortality experience is used to conduct detailed comparisons at pensioner ages, having first established a common basis for comparison across all models. The model comparison is then extended to include the England & Wales female experience and both the male and female USA mortality experiences over a wider age range, encompassing also the working ages.

The paper presents a reinterpretation of the model underpinning the Lee-Carter methodology for forecasting mortality (and other vital) rates. A parallel methodology based on generalized linear modelling is introduced. The use of residual plots is proposed for both methods to aid the assessment of the goodness of fit. The two methods are compared in terms of structure and assumptions. They are then compared through an analysis of the gender- and age-specific mortality rates for England and Wales over the period 1950-1998 and through a consideration of the forecasts generated by the two methods. The paper also compares different approaches to the forecasting of life expectancy and considers the effectiveness of the Coale-Guo method for extrapolating mortality rates to the oldest ages. Copyright 2003 Royal Statistical Society.

This paper presents a statistical model underlying the chain-ladder technique. This is related to other statistical approaches to the chain-ladder technique which have been presented previously. The statistical model is cast in the form of a generalised linear model, and a quasi-likelihood approach is used. It is shown that this enables the method to process negative incremental claims. It is suggested that the chain-ladder technique represents a very narrow view of the possible range of models.

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The authors review the applications of generalized linear models to actuarial problems. This rich class of statistical model has been successfully applied in recent years to a wide range of problems, involving mortality, multiple-state models, lapses, premium rating and reserving. Selective examples of these applications are presented.

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