A hierarchical model for the joint mortality analysis of pension scheme data with missing covariates

Francesco Ungolo, Torsten Kleinow, Angus Smith Macdonald

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
56 Downloads (Pure)


A hierarchical model is developed for the joint mortality analysis of pension scheme datasets. The proposed model allows for a rigorous statistical treatment of missing data. While our approach works for any missing data pattern, we are particularly interested in a scenario where some covariates are observed for members of one pension scheme but not the other. Therefore, our approach allows for the joint modelling of datasets which contain different information about individual lives. The proposed model generalizes the specification of parametric models when accounting for covariates. We consider parameter uncertainty using Bayesian techniques. Model parametrization is analysed in order to obtain an efficient MCMC sampler, and address model selection. The inferential framework described here accommodates any missing-data pattern, and turns out to be useful to analyse statistical relationships among covariates. Finally, we assess the financial impact of using the covariates, and of the optimal use of the whole available sample when combining data from different mortality experiences.

Original languageEnglish
Pages (from-to)68-84
Number of pages17
JournalInsurance: Mathematics and Economics
Early online date14 Jan 2020
Publication statusPublished - Mar 2020


  • Bayesian inference
  • Longevity risk
  • MCMC
  • Missing data
  • Model selection
  • Mortality
  • Mortality models with covariates
  • Survival model

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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