European Actuarial Journal

, Volume 3, Issue 1, pp 191–201 | Cite as

Approximations for quantiles of life expectancy and annuity values using the parametric improvement rate approach to modelling and projecting mortality

  • Michel Denuit
  • Steven Haberman
  • Arthur E. Renshaw
Original Research Paper


In this paper, we develop accurate approximations for medians of life expectancy and life annuity pure premiums viewed as functions of future mortality trends as predicted by parametric models of the improvement rates in mortality. Numerical illustrations show that the comonotonic approximations perform well in this case, which suggests that they can be used in practice to evaluate the consequences of the uncertainty in future death rates. Prediction intervals based on 5 and 95 % quantiles are also considered but appear to be wider compared to simulated ones. This provides the practitioner with a conservative shortcut, thereby avoiding the problem of simulations within simulations in, for instance, Solvency 2 calculations.


Life annuity Life expectancy Mortality projection Comonotonicity Simulation 



The authors would like to express their gratitude to an anonymous Referee whose comments have been extremely useful to revise a previous version of the present work. The financial support of PARC “Stochastic Modelling of Dependence” 2012–2017 awarded by the Communauté française de Belgique is gratefully acknowledged by Michel Denuit.


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Copyright information

© DAV / DGVFM 2013

Authors and Affiliations

  • Michel Denuit
    • 1
  • Steven Haberman
    • 2
  • Arthur E. Renshaw
    • 2
  1. 1.Universite Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Cass Business SchoolCity University LondonLondonUK

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