Lifetime Dependence Modelling using the Truncated Multivariate Gamma Distribution
Daniel Alai (),
Zinoviy Landsman () and
Michael Sherris ()
Additional contact information Daniel Alai: ARC Centre of Excellence in Population Ageing Research, Australian School of Business, University of New South Wales
Zinoviy Landsman: Departmant of Statistics, University of Haifa
Michael Sherris: School of Risk and Actuarial Studies and ARC Centre of Excellence in Population Ageing Research, Australian School of Business, University of New South Wales
Systematic improvements in mortality results in dependence in the survival distributions of insured lives. This is not allowed 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 on the valuation of a portfolio, or cohort, of annuitants with similar risk characteristics is demonstrated by applying the model to annuity valuation. The 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.