Lifetime Dependence Modelling Using a Truncated Multivariate Gamma Distribution
Daniel H. Alai
Australian School of Business at UNSW
University of Haifa, Department of Statistics
University of New South Wales - ARC Centre of Excellence in Population Ageing Research and School of Risk and Actuarial Studies
April 2, 2012
UNSW Australian School of Business Research Paper No. AIPAR 2012/3
Systematic improvements in mortality 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.
Number of Pages in PDF File: 24
Keywords: Systematic Longevity Risk, Dependence, Multivariate Gamma, Lifetime Distribution, Annuity Valuation
JEL Classification: G22, G32, C13, C02working papers series
Date posted: April 2, 2012 ; Last revised: March 26, 2013
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