Lifetime dependence modelling using a truncated multivariate gamma distribution

Daniel H. Alai, Zinoviy Landsman, Michael Sherris

Research output: Contribution to journalArticlepeer-review


Systematic improvements in mortality increases dependence in the survival distributions of insured lives, which is not accounted for in standard life tables and actuarial models used for annuity pricing and reserving. Systematic longevity risk also undermines the law of large numbers, a law that is relied on in the risk management of life insurance and annuity portfolios. This paper applies a multivariate gamma distribution to incorporate dependence. Lifetimes are modelled using a truncated multivariate gamma distribution that induces dependence through a shared gamma distributed component. Model parameter estimation is developed based on the method of moments and generalized to allow for truncated observations. The impact of dependence within a portfolio, or cohort, of lives with similar risk characteristics is demonstrated by applying the model to annuity valuation. Dependence is shown to have a significant impact on the risk of the annuity portfolio as compared with traditional actuarial methods that implicitly assume independent lifetimes.

Original languageEnglish
Pages (from-to)542-549
Number of pages8
JournalInsurance: Mathematics and Economics
Issue number3
StatePublished - May 2013

Bibliographical note

Funding Information:
The authors would like to acknowledge the financial support of ARC Linkage Grant Project LP0883398 Managing Risk with Insurance and Superannuation as Individuals Age with industry partners PwC, APRA, and the World Bank, as well as the support of the Australian Research Council Centre of Excellence in Population Ageing Research (project number CE110001029).


  • Annuity valuation
  • Dependence
  • Lifetime distribution
  • Multivariate gamma
  • Systematic longevity risk

ASJC Scopus subject areas

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


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