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Modelling stochastic mortality for dependent lives

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  • Luciano, Elisa
  • Spreeuw, Jaap
  • Vigna, Elena

Abstract

Stochastic mortality, i.e. modelling death arrival via a jump process with stochastic intensity, is gaining an increasing reputation as a way to represent mortality risk. This paper is a first attempt to model the mortality risk of couples of individuals, according to the stochastic intensity approach. Dependence between the survival times of the members of a couple is captured by an Archimedean copula. We also provide a methodology for fitting the joint survival function by working separately on the (analytical) marginals and on the (analytical) copula. First, we provide a sample-based calibration for the intensity, using a time-homogeneous, non mean-reverting, affine process: this gives the marginal survival functions. Then we calibrate and select the best fit copula according to the Wang and Wells [Wang, W., Wells, M.T., 2000b. Model selection and semiparametric inference for bivariate failure-time data. J. Amer. Statis. Assoc. 95, 62-72] methodology for censored data. By coupling the calibrated marginals with the best fit copula, we obtain a joint survival function, which incorporates the stochastic nature of mortality improvements. We apply the methodology to a well known insurance data set, using a sample generation. The best fit copula turns out to be one listed in [Nelsen, R.B., 2006. An Introduction to Copulas, Second ed. In: Springer Series], which implies not only positive dependence, but dependence increasing with age.

Suggested Citation

  • Luciano, Elisa & Spreeuw, Jaap & Vigna, Elena, 2008. "Modelling stochastic mortality for dependent lives," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 234-244, October.
  • Handle: RePEc:eee:insuma:v:43:y:2008:i:2:p:234-244
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    More about this item

    Keywords

    Dependent lives Best fit copula Stochastic mortality Joint survival function Generation effect Time-dependent association;

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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