Modelling stochastic mortality for dependent lives

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 approa...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2008-10, Vol.43 (2), p.234-244
Main Authors: Luciano, Elisa, Spreeuw, Jaap, Vigna, Elena
Format: Article
Language:English
Subjects:
Best fit copula
Couples
Dependent lives
Dependent lives Best fit copula Stochastic mortality Joint survival function Generation effect Time-dependent association
Generation effect
Insurance
Joint survival function
Measurement
Methodology
Mortality
Risk
Risk management
Stochastic models
Stochastic mortality
Studies
Survival
Time
Time-dependent association
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Summary: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.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2008.06.005