European Actuarial Journal

, Volume 9, Issue 2, pp 483–518 | Cite as

Mortality projections for non-converging groups of populations

  • Lukas Josef HahnEmail author
  • Marcus Christian Christiansen
Original Research Paper


We propose a nested multi-population mortality projection model in which the forces of mortality are modelled via an extended version of the Cairns–Blake–Dowd model for middle and higher ages, and the resulting model parameters are forecast using a vector error correction model. Dependencies between different populations are accounted for by the joint parameter dynamics through lag coefficients (short-term predictability between the marginals), cointegration relations (long-run equilibriums), and error terms (correlated shocks). Bayesian inference assures integrated estimation and prediction of all hierarchical parameters in one step and allows for quantifying the underlying joint uncertainty. Our hierarchical set-up—yet flexible and easily interpretable—leads to a wider range of biologically plausible forecasts including, e.g., long-lasting, possibly varying discrepancies or phases of temporal divergence. We study two empirical examples in European mortality which suggest that the common a priori coherence assumption in actuarial projection models is too restrictive.


Multi-population mortality forecasting Heterogeneous collection of populations Extended Cairns–Blake–Dowd model Vector error correction model Bayesian estimation Markov chain Monte Carlo 


Supplementary material

13385_2019_213_MOESM1_ESM.pdf (3.2 mb)
Supplementary material 1 (pdf 3235 KB)


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Copyright information

© EAJ Association 2019

Authors and Affiliations

  1. 1.Big Data LabSV SparkassenVersicherungStuttgartGermany
  2. 2.Institut für MathematikCarl von Ossietzky Universität OldenburgOldenburgGermany

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