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Lifetime Dependence Modelling using the Truncated Multivariate Gamma Distribution

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • Daniel Alai & Zinoviy Landsman & Michael Sherris, 2012. "Lifetime Dependence Modelling using the Truncated Multivariate Gamma Distribution," Working Papers 201211, ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales.
    • Handle: RePEc:asb:wpaper:201211
    as

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    File URL: http://cepar.edu.au/media/79139/12_lifetime_dependence_modelling_using_the_truncated_multivariate.pdf
    File Function: First version, 2012
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    References listed on IDEAS

    as
    1. Varadhan, Ravi & Gilbert, Paul, 2009. "BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i04).
    2. Furman, Edward & Landsman, Zinoviy, 2005. "Risk capital decomposition for a multivariate dependent gamma portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 635-649, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Systematic longevity risk; dependence; multivariate gamma; lifetime distribution; annuity valuation;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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