Steven Haberman

Lee–Carter mortality forecasting with age-specific enhancement

Abstract We investigate the feasibility of constructing mortality forecasts on the basis of the first two sets of single value decomposition vectors, rather than just on the first such set of vectors, as in the established Lee–Carter (Gaussian) approach to mortality forecasting. Three applications are presented and the resulting forecasts compared with those constructed using two similar approaches based on generalised linear and bilinear models with Poisson error structures.

Lee–Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections

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.

Optimal investment strategies and risk measures in defined contribution pension schemes

In this paper, we analyse the investment allocation and the downside risk faced by the retiring member of a defined contribution pension scheme, where optimal investment strategies (derived from a dynamic programming approach) have been adopted. The behaviour of the optimal investment strategy is analysed when changing the disutility function and the correlation between the assets. Three different risk measures are considered in analysing the final net replacement ratios achieved by the member: the probability of failing the target, the mean shortfall and a Value at Risk type measure. The replacement ratios encompass the financial and annuitization risks faced by the retiree. We consider the relationship between the risk aversion of the member and these different risk measures in order to understand better the choices confronting different categories of scheme member. We consider the case of a 2 assets portfolio, where the asset returns are correlated and consider the sensitivity of the results to the level of the correlation coefficient.

On the forecasting of mortality reduction factors

Abstract Ways in which the so-called Lee–Carter time series approach to forecasting mortality patterns can be modified to forecast the possible future behaviour of mortality reduction factors (RFs) are described. A comparison is drawn with an alternative regression type approach to the forecasting of mortality RFs, based on the same model structure. Case studies, illustrating different aspects of the methodology, making use of both the more recent mortality experience of UK male pensioner lives and the historical mortality experience of UK male annuitants, are presented.

Generalized linear models and actuarial science

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.

Valuation of guaranteed annuity conversion options

In this note we introduce a theoretical model for the pricing and valuation of guaranteed annuity conversion options associated with certain deferred annuity pension-type contracts in the UK. The valuation approach is based on the similarity between the payoff structure of the contract and a call option written on a coupon-bearing bond. The model makes use of a one-factor Heath–Jarrow–Morton framework for the term structure of interest rates. Numerical results are investigated and the sensitivity of the price of the option to changes in the key parameters is also analyzed.

Dynamic approaches to pension funding

Abstract The paper presents a dynamic model of pension funding for a defined benefit occupational pension scheme. Two types of risk are introduced concerned respectively with the stability and security of funding: the ‘ contribution rate ’ risk and the ‘ solvency ’ risk. An objective function is introduced to allow the simultaneous minimization of these two risks. The paper derives optimal funding control procedures for the contribution rate subject to specified constraints.

The seasonal variation in mortality from cerebrovascular disease

The frequency distribution of deaths from cerebrovascular disease in England and Wales in 1975 by month of occurrence is described. The distribution is compared with that for related diseases, in particular ischaemic heart disease, hypertensive disease, pneumonia and bronchitis. The principal feature in all these diseases is high mortality in winter and spring and low mortality in late summer, but the range of variation is wider for pneumonia and bronchitis. The seasonal distribution of cerebrovascular disease death is similar in both sexes, all ages at death and for deaths at home and deaths in a hospital or institution. For both sexes the proportion of cerebrovascular disease deaths occurring at home increases significantly with age at death. Four hypotheses are examined to explain this characteristic seasonal mortality pattern, which is related inversely to ambient temperature, and similar to the seasonal pattern of the incidence and prevalence of cerebrovascular disease.

Optimal investment strategy for defined contribution pension schemes

Abstract We analyse the financial risk in a defined contribution pension scheme, applying dynamic programming techniques to find an optimal investment strategy for the scheme member. We use a series of interim targets and a target at retirement linked to the desired net replacement ratio. We consider both the investment risk and the annuitisation risk faced by the individual and specifically consider the properties of the so-called “lifestyle” investment strategies. The principal results concern the suitability of the lifestyle strategy and the large variability of the level of pension achieved at retirement in the case of a variable annuity conversion rate.

Projecting Mortality Trends

Abstract The sustained reduction in mortality rates and its systematic underestimation has been attracting the significant interest of researchers in recent times because of its potential impact on population size and structure, social security systems, and (from an actuarial perspective) the life insurance and pensions industry worldwide. Despite the number of papers published in recent years, a comprehensive review has not yet been developed. This paper attempts to be the starting point for that review, highlighting the importance of recently published research—most of the references cited span the last 10 years—and covering the main methodologies that have been applied to the projection of mortality rates in the United Kingdom and the United States. A comparative review of techniques used in official population projections, actuarial applications, and the most influential scientific approaches is provided. In the course of the review an attempt is made to identify common themes and similarities in methods and results. In both official projections and actuarial applications there is some evidence of systematic overestimation of mortality rates. Models developed by academic researchers seem to reveal a trade-off between the plausibility of the projected age pattern and the ease of measuring the uncertainty involved. The Lee-Carter model is one approach that appears to solve this apparent dilemma. There is a broad consensus across the resulting projections: (1) an approximately log-linear relationship between mortality rates and time, (2) decreasing improvements according to age, and (3) an increasing trend in the relative rate of mortality change over age. In addition, evidence suggests that excessive reliance on expert opinion—present to some extent in all methods—has led to systematic underestimation of mortality improvements.