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Mortality projections for non-converging groups of populations

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Abstract

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.

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Notes

  1. The code is available upon request to the corresponding author.

  2. For our application, we directly present the model with a constant deterministic trend per marginal time series. In general, the VECM allows for \(d \in {\mathbb {N}}\) deterministic trends through \(\phi D_t\) with time-varying constants \(D_t \in {\mathbb {R}}^{d}\) and parameter matrix \(\phi \in {\mathbb {R}}^{m \times d}\), e.g. by setting \(D_t = (1,t)^\prime \) and \(d=2\) to include time-varying trends. The matrix notation \({\varPhi }\) and the following Bayesian inference can be generalised accordingly.

  3. The code is available upon request to the corresponding author.

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Authors and Affiliations

  1. Big Data Lab, SV SparkassenVersicherung, Stuttgart, Germany

    Lukas Josef Hahn

  2. Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany

    Marcus Christian Christiansen

Authors
  1. Lukas Josef Hahn
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  2. Marcus Christian Christiansen
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Correspondence to Lukas Josef Hahn.

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Hahn, L.J., Christiansen, M.C. Mortality projections for non-converging groups of populations. Eur. Actuar. J. 9, 483–518 (2019). https://doi.org/10.1007/s13385-019-00213-1

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  • DOI: https://doi.org/10.1007/s13385-019-00213-1

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