Modelling stochastic mortality for dependent lives

Luciano, E., Spreeuw, J. & Vigna, E. (2008). Modelling stochastic mortality for dependent lives. Insurance: Mathematics and Economics, 43(2), pp. 234-244. doi: 10.1016/j.insmatheco.2008.06.005

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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.

Item Type: Article
Additional Information: © 2008 Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ NOTICE: this is the author's version of a work that was accepted for publication in Insurance: Mathematics and Economics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Insurance: Mathematics and Economics, Volume 43, Issue 2, October 2008, Pages 234-244, http://dx.doi.org/10.1016/j.insmatheco.2008.06.005.
Uncontrolled Keywords: Dependent lives; Best fit copula; Stochastic mortality; Joint survival function; Generation effect; Time-dependent association
Subjects: H Social Sciences > HA Statistics
Divisions: Cass Business School > Faculty of Actuarial Science & Insurance
URI: http://openaccess.city.ac.uk/id/eprint/12895

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