Computational Management Science

, Volume 11, Issue 1–2, pp 111–137 | Cite as

Computational framework for longevity risk management

  • Valeria D’Amato
  • Steven Haberman
  • Gabriella Piscopo
  • Maria Russolillo
Original Paper


Longevity risk threatens the financial stability of private and government sponsored defined benefit pension systems as well as social security schemes, in an environment already characterized by persistent low interest rates and heightened financial uncertainty. The mortality experience of countries in the industrialized world would suggest a substantial age-time interaction, with the two dominant trends affecting different age groups at different times. From a statistical point of view, this indicates a dependence structure. It is observed that mortality improvements are similar for individuals of contiguous ages (Wills and Sherris, Integrating financial and demographic longevity risk models: an Australian model for financial applications, Discussion Paper PI-0817, 2008). Moreover, considering the dataset by single ages, the correlations between the residuals for adjacent age groups tend to be high (as noted in Denton et al., J Population Econ 18:203–227, 2005). This suggests that there is value in exploring the dependence structure, also across time, in other words the inter-period correlation. In this research, we focus on the projections of mortality rates, contravening the most commonly encountered dependence property which is the “lack of dependence” (Denuit et al., Actuarial theory for dependent risks: measures. Orders and models, Wiley, New York, 2005). By taking into account the presence of dependence across age and time which leads to systematic over-estimation or under-estimation of uncertainty in the estimates (Liu and Braun, J Probability Stat, 813583:15, 2010), the paper analyzes a tailor-made bootstrap methodology for capturing the spatial dependence in deriving confidence intervals for mortality projection rates. We propose a method which leads to a prudent measure of longevity risk, avoiding the structural incompleteness of the ordinary simulation bootstrap methodology which involves the assumption of independence.


Longevity risk management Bootstrap techniques 



The authors would like to express their gratitude to the participants at \(9\mathrm{th}\) International Conference on Computational Management Science whose comments have been extremely useful in helping us to revise a previous version of the present work.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Valeria D’Amato
    • 1
  • Steven Haberman
    • 2
  • Gabriella Piscopo
    • 3
  • Maria Russolillo
    • 1
  1. 1.Department of Economics and StatisticsUniversity of SalernoFiscianoItaly
  2. 2.Faculty of Actuarial Science and Insurance, Cass Business SchoolCity UniversityLondonUK
  3. 3.Department of Economics and Quantitative MethodsUniversity of GenoaGenoaItaly

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