Modelling stochastic mortality for dependent lives
AbstractStochastic mortality, i.e. modelling death arrival via a jump process with stochastic intensity, is gaining increasing reputation as a way to rep- resent mortality risk. This paper represents a .rst attempt to model the mortality risk of couples of individuals, according to the stochastic inten- sity approach. We extend to couples the Cox processes set up, namely the idea that mortality is driven by a jump process whose intensity is itself a stochastic process, proper of a particular generation within each gen- der. 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) copula and the (analytical) mar- gins. First, we calibrate and select the best fit copula according to the methodology of Wang and Wells (2000b) for censored data. Then, we provide a sample-based calibration for the intensity, using a time- homogeneous, non mean-reverting, affine process: this gives the marginal survival functions. By coupling the best fit copula with the calibrated mar- gins we obtain a joint survival function which incorporates the stochastic nature of mortality improvements. Several measures of time dependent association can be computed out of it. We apply the methodology to a well known insurance dataset, using a sample generation. The best fit copula turns out to be a Nelsen one, which implies not only positive dependency, but dependency increasing with age.
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Bibliographic InfoPaper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 43.
Length: 34 pages
Date of creation: 2007
Date of revision:
stochastic mortality; bivariate mortality; copula functions; longevity risk.;
Other versions of this item:
- 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.
- Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2007. "Modelling Stochastic Mortality for Dependent Lives," CeRP Working Papers 58, Center for Research on Pensions and Welfare Policies, Turin (Italy).
- G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-11-24 (All new papers)
- NEP-ECM-2007-11-24 (Econometrics)
- NEP-HEA-2007-11-24 (Health Economics)
- NEP-RMG-2007-11-24 (Risk Management)
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- Elisa Luciano & Elena Vigna, 2006.
"Non mean reverting affne processes for stochastic mortality,"
Carlo Alberto Notebooks, Collegio Carlo Alberto
30, Collegio Carlo Alberto.
- Elisa Luciano & Elena Vigna, 2005. "Non mean reverting affine processes for stochastic mortality," ICER Working Papers - Applied Mathematics Series, ICER - International Centre for Economic Research 4-2005, ICER - International Centre for Economic Research.
- Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
- Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
- repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
- Manatunga, Amita K. & Oakes, David, 1996. "A Measure of Association for Bivariate Frailty Distributions," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 60-74, January.
- Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
- Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
- Christian Genest & Jean-FranÃ§ois Quessy & Bruno RÃ©millard, 2006. "Goodness-of-fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 337-366.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 1999.
"Transform Analysis and Asset Pricing for Affine Jump-Diffusions,"
NBER Working Papers
7105, National Bureau of Economic Research, Inc.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, Econometric Society, vol. 68(6), pages 1343-1376, November.
- Elisa Luciano & Luca Regis & Elena Vigna, 2011. "Delta and Gamma hedging of mortality and interest rate risk," ICER Working Papers - Applied Mathematics Series, ICER - International Centre for Economic Research 01-2011, ICER - International Centre for Economic Research.
- Antonio Romero Medina & Mateo Triossi, 2007.
"Games of capacities : a (close) look to Nash Equilibria,"
Economics Working Papers
we075933, Universidad Carlos III, Departamento de EconomÃa.
- Antonio Romero-Medina & Matteo Triossi, 2011. "Games with capacity manipulation : incentives and Nash equilibria," Economics Working Papers we1125, Universidad Carlos III, Departamento de EconomÃa.
- Antonio Romero-Medina & Matteo Triossi, 2011. "Games with Capacity Manipulation: Incentives and Nash Equilibria," Documentos de Trabajo, Centro de EconomÃa Aplicada, Universidad de Chile 280, Centro de EconomÃa Aplicada, Universidad de Chile.
- Antonio Romero-Medina & Matteo Triossi, 2007. "Games of Capacities: A (Close) Look to Nash Equilibria," Carlo Alberto Notebooks, Collegio Carlo Alberto 52, Collegio Carlo Alberto.
- Luciano, Elisa & Regis, Luca & Vigna, Elena, 2012. "Delta–Gamma hedging of mortality and interest rate risk," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 402-412.
- Carsten Schröder, 2010.
"Profitability of Pension Contributions: Evidence from Real-Life Employment Biographies,"
Discussion Papers of DIW Berlin
1057, DIW Berlin, German Institute for Economic Research.
- SchrÃ¶der, Carsten, 2012. "Profitability of pension contributions â€“ evidence from real-life employment biographies," Journal of Pension Economics and Finance, Cambridge University Press, Cambridge University Press, vol. 11(03), pages 311-336, July.
- Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2012. "Evolution of coupled lives' dependency across generations and pricing impact," Carlo Alberto Notebooks, Collegio Carlo Alberto 258, Collegio Carlo Alberto.
- Wang, Chou-Wen & Huang, Hong-Chih & Hong, De-Chuan, 2013. "A feasible natural hedging strategy for insurance companies," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 532-541.
- Lopez, Olivier, 2012. "A generalization of the Kaplan–Meier estimator for analyzing bivariate mortality under right-censoring and left-truncation with applications in model-checking for survival copula models," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 505-516.
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