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Case study of Swiss mortality using Bayesian modeling

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Abstract

Most mortality models to date in life insurance have inconsistent modeling assumptions between past and future survival probabilities. This paper aims at correcting this inconsistency by introducing a Bayesian framework for the joint modeling of past survival probabilities and the forecasting of future survival probabilities. To that end, the Bayesian modeling framework introduced considers both the uncertainty in the populations counts (random effects) as well as the uncertainty in the survival probability surface (systemic effects). In particular, the model uses an n-dimensional latent risk factor process to encode the survival probability surface, taking into account its intrinsic dependencies. We use the model for a case study of Swiss mortality. The case study shows that the model fits well to Swiss data and systemic events in the Swiss survival probability surface are captured by the model. The Swiss case study also exhibits the different rate of improvements in mortality for different age groups of the Swiss population.

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Notes

  1. www.mortality.org.

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Authors and Affiliations

  1. RiskLab Switzerland, Department of Mathematics, ETH Zurich, 8092, Zurich, Switzerland

    Laurent J. Huber & Mario V. Wüthrich

Authors
  1. Laurent J. Huber
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  2. Mario V. Wüthrich
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Correspondence to Laurent J. Huber.

Appendix: Optimal basis fit for other countries

Appendix: Optimal basis fit for other countries

See Tables 6 and 7.

Table 6 France: summary of values for the log-likelihood and the BIC for the optimal \(\mathcal {I}_n\) with \(2 \le n \le 7\) for females (above) and males (below)
Full size table
Table 7 Austria: summary of values for the log-likelihood and the BIC for the optimal \(\mathcal {I}_n\) with \(2 \le n \le 7\) for females (above) and males (below)
Full size table

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Huber, L.J., Wüthrich, M.V. Case study of Swiss mortality using Bayesian modeling. Eur. Actuar. J. 6, 25–59 (2016). https://doi.org/10.1007/s13385-015-0119-2

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