Modelling stochastic mortality for dependent lives

Stochastic mortality, i.e. modelling death arrival via a jump process with stochastic intensity, is gaining 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 (2000b) 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 (2006), which implies not only positive dependence, but dependence increasing with age.