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The Actuary The magazine of the Institute & Faculty of Actuaries

Modelling mortality and longevity

Mortality is on the move and actuaries’ advice must not just keep up but stay ahead. Help by the profession has been posted in the last few weeks: a special supplement to the British Actuarial Journal (supplement to Volume 15) on mortality and longevity modelling. The supplement comprises review papers of the most up-to-date research findings together with a critical assessment of modelling and projection methods from leading authorities across the interrelated disciplines of biomedical and health research as well as demography and actuarial science.

The supplement records a selection of papers presented at the conference, Joining Forces on Mortality and Longevity, hosted by the profession in Edinburgh in October 2009. The conference was organised around three inter-related themes: drivers of change in longevity, how successive cohorts differ and why; and the connections between aggregate population mortality and individual risk characteristics. These themes were identified as of particular relevance to informing actuaries’ opinions by the Mortality Research Steering Group, which organised the conference and which, a year before, had presented a Report on Scoping Mortality Research (sessional meeting paper to Institute of Actuaries, September 2008).

There are 11 papers in the issue together with a discursive editorial. Diana Kuh and colleagues open with a comprehensive Review of Life Time Risk Factors for Mortality. Their paper marshals research on such factors as environment, lifestyle, body size, physical ability and cognitive function to show how each alters the mortality experience of individuals, not just when currently exposed to such factors but at times long after exposure — with linkages reported between elevated mortality late in life and early life experiences.

The importance of individual risk characteristics in mortality disposes one to seek cohort influences in population mortality trends. Carol Jagger et al take up this theme in their paper, Cohort Differences in Mortality and Morbidity. They review the papers presented at the conference on the cohort theme and, in addition, give an overview of research that suggests that the increases in life expectancies witnessed in recent decades are largely increases in healthy life expectancies.

Next follows papers that provide evidence for the cohort effect at aggregate population levels. David Forfar reminds us of the statistical evidence in the populations of Scotland as well as England and Wales and shows the consequences of incorporating a cohort effect in mortality projections. Alison O’Connell and Kim Dunstan report finding evidence that the UK ‘golden generation’ has brought along their mortality improvement as emigrants to New Zealand.

Maria Reinert-Azambuja highlights the complex connections that could be posited to exist when early life experiences can impact later life mortality, with her speculative paper suggesting a link between heart disease late in life and exposure to influenza early in life.

Mike Murphy’s paper, The ‘Golden Generations’ in Historical Context, challenges the ‘cohort effect’ and how it is currently modelled. He suggests that the observed ‘cohort effect’ does not reflect changing mortality of the average person in the population but the changing mix of two separate populations within the overall population that have a material mortality differential.

The next paper, by Mariachiara Di Cesare and Mike Murphy, shows that, inter alia, mortality projections by individual cause of death can be improved by using period-based models for those causes of death that are primarily driven by calendar year effects and by employing cohort-based models when the underlying driving factor is primarily related to long-term past exposures that are changing in time.

The last four papers treat different themes. First, Eugene Milne proposes a new mathematical model of ageing and mortality. The model, in the classic tradition of mathematical and actuarial science, is a simple but well-motivated model of individual mortality risk that, he shows, is capable of reproducing mortality curves of human populations and those of other species when heterogeneity of risk within the population is captured by parameter variability.

Second, Gordon Woo and colleagues consider how mortality risk might be modelled on a prospective basis, in a parallel to how catastrophe risk is currently modelled. Eschewing the dominant approach of statistically modelling past mortality data and then trying to project rates into the future, they outline all the factors that affect future rates and attempt to model each factor stochastically, from advances in geroscience to new drug discoveries to changes in personal lifestyles.

Third, Bridget Browne and colleagues address themselves directly to the problem of developing a stochastic model of future mortality variability that might determine the capital required for an annuity portfolio to satisfy the requirements of the regulator. Their proposed model can be bolted on to any deterministic model of future expected mortality rates. They recommend, with supporting rationale, an absolute minimum level of volatility. This paper is of significant practical importance to actuaries developing such models.

Stephen Richards provides the final paper, in which he considers some issues that arise for actuaries in applying some of the insights gained from presentations at the conference.


Dr Shane Whelan is a lecturer at University College Dublin, a council member of the Society of Actuaries in Ireland, and a fellow of the Institute and Faculty of Actuaries