Lifetime dependence modelling using a truncated multivariate gamma distribution

Daniel H. Alai, Zinoviy Landsman and Michael Sherris

Insurance: Mathematics and Economics, 2013, vol. 52, issue 3, 542-549

Abstract: 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.

Keywords: Systematic longevity risk; Dependence; Multivariate gamma; Lifetime distribution; Annuity valuation (search for similar items in EconPapers)
JEL-codes: C02 C13 G22 G32 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:52:y:2013:i:3:p:542-549

DOI: 10.1016/j.insmatheco.2013.03.011

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