Modelling stochastic mortality for dependent lives

Elisa Luciano, Jaap Spreeuw and Elena Vigna

Insurance: Mathematics and Economics, 2008, vol. 43, issue 2, 234-244

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.

Keywords: Dependent; lives; Best; fit; copula; Stochastic; mortality; Joint; survival; function; Generation; effect; Time-dependent; association (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (34)

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Related works:
Working Paper: Modelling stochastic mortality for dependent lives (2007)
Working Paper: Modelling Stochastic Mortality for Dependent Lives (2007)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:43:y:2008:i:2:p:234-244

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