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The joint mortality of couples in continuous time

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  • Jevtić, P.
  • Hurd, T.R.

Abstract

This paper introduces a probabilistic framework for the joint survivorship of couples in the context of dynamic stochastic mortality models. The death of one member of a couple can have either deterministic or stochastic effects on the other; our new framework gives an intuitive and flexible pairwise cohort-based probabilistic mechanism that can account for both. It is sufficiently flexible to allow modelling of effects that are short-term (called the broken-heart effect) and/or long-term (named life circumstances bereavement). In addition, it can account for the state of health of both the surviving and the dying spouse and can allow for dynamic and asymmetric reactions of varying complexity. Finally, it can accommodate the pairwise dependence of mortality intensities before the first death. Analytical expressions for bivariate survivorship in representative models are given, and their sensitivity analysis is performed for benchmark cases of old and young couples. Simulation and estimation procedures are provided that are straightforward to implement and lead to consistent parameter estimation on synthetic dataset of 10000 pairs of death times for couples.

Suggested Citation

  • Jevtić, P. & Hurd, T.R., 2017. "The joint mortality of couples in continuous time," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 90-97.
    • Handle: RePEc:eee:insuma:v:75:y:2017:i:c:p:90-97
    DOI: 10.1016/j.insmatheco.2017.05.002
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    References listed on IDEAS

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    1. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2016. "Spouses’ Dependence across Generations and Pricing Impact on Reversionary Annuities," Risks, MDPI, vol. 4(2), pages 1-18, May.
    2. LUCIANO, Elisa & VIGNA, Elena, 2008. "Mortality risk via affine stochastic intensities: calibration and empirical relevance," MPRA Paper 59627, University Library of Munich, Germany.
    3. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    4. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    5. Jianxi Su & Edward Furman, 2016. "Multiple risk factor dependence structures: Distributional properties," Papers 1607.04739, arXiv.org.
    6. 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.
    7. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    8. 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.
    9. Min Ji & Mary Hardy & Johnny Siu-Hang Li, 2011. "Markovian Approaches to Joint-Life Mortality," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(3), pages 357-376.
    10. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
    11. Spreeuw, Jaap & Owadally, Iqbal, 2013. "Investigating the Broken-Heart Effect: a Model for Short-Term Dependence between the Remaining Lifetimes of Joint Lives," Annals of Actuarial Science, Cambridge University Press, vol. 7(2), pages 236-257, September.
    12. Qian, Linyi & Wang, Wei & Wang, Rongming & Tang, Yincai, 2010. "Valuation of equity-indexed annuity under stochastic mortality and interest rate," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 123-129, October.
    13. Jianxi Su & Edward Furman, 2016. "Multiple risk factor dependence structures: Copulas and related properties," Papers 1610.02126, arXiv.org.
    14. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2012. "Evolution of coupled lives' dependency across generations and pricing impact," Carlo Alberto Notebooks 258, Collegio Carlo Alberto.
    15. 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.
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    Cited by:

    1. Kira Henshaw & Corina Constantinescu & Olivier Menoukeu Pamen, 2020. "Stochastic Mortality Modelling for Dependent Coupled Lives," Risks, MDPI, vol. 8(1), pages 1-28, February.
    2. Rui Fang & Xiaohu Li, 2018. "Some Results on Measures of Interaction between Paired Risks," Risks, MDPI, vol. 6(3), pages 1-15, August.

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