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Love and Death : A Freund Model with Frailty


  • Christian Gouriéroux

    () (Crest, University of Toronto)

  • Yang Lu

    () (SCOR and Crest)


We introduce new models for analyzing the mortality dependence between individuals in a couple. The mortality risk dependence is usually taken into account in the actuarial literature by introducing an Archimedean copula. This practice implies symmetric effects on the remaining lifetime of the surviving spouse. The new model allows for both asymmetric reactions by means of a Freund model, and risk dependence by means of an unobservable common risk factor (or frailty). These models allow for distinguishing in the lifetime dependence the component due to common lifetime (frailty) from the broken-heart syndrome (Freund model). The model is applied to insurance products such as joint life policy, last survivor insurance, or contracts with reversionary annuities

Suggested Citation

  • Christian Gouriéroux & Yang Lu, 2013. "Love and Death : A Freund Model with Frailty," Working Papers 2013-09, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2013-09

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    References listed on IDEAS

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    2. Darrell Duffie & Andreas Eckner & Guillaume Horel & Leandro Saita, 2009. "Frailty Correlated Default," Journal of Finance, American Finance Association, vol. 64(5), pages 2089-2123, October.
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    5. Nihtilä, E. & Martikainen, P., 2008. "Institutionalization of older adults after the death of a spouse," American Journal of Public Health, American Public Health Association, vol. 98(7), pages 1228-1234.
    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. 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.
    8. 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.
    9. Jinfeng Xu & John D. Kalbfleisch & Beechoo Tai, 2010. "Statistical Analysis of Illness–Death Processes and Semicompeting Risks Data," Biometrics, The International Biometric Society, vol. 66(3), pages 716-725, September.
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    11. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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    Cited by:

    1. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    2. Christian Gourieroux & Yang Lu, 2013. "Long Term Care and Longevity," Working Papers 2013-16, Center for Research in Economics and Statistics.
    3. Mercedes Ayuso & Jorge Miguel Bravo & Robert Holzman, 2018. "Getting Life Expectancy Estimates Right for Pension Policy: Period versus Cohort Approach," CESifo Working Paper Series 7349, CESifo.
    4. Kira Henshaw & Corina Constantinescu & Olivier Menoukeu Pamen, 2020. "Stochastic Mortality Modelling for Dependent Coupled Lives," Risks, MDPI, Open Access Journal, vol. 8(1), pages 1-28, February.
    5. van den Berg, Gerard J. & Drepper, Bettina, 2018. "A Unique Bond: Twin Bereavement and Lifespan Associations of Identical and Fraternal Twins," IZA Discussion Papers 11448, Institute of Labor Economics (IZA).

    More about this item


    Life Insurance; Coupled Lives; Frailty; Freund Model; Broken-Heart; Copula; Last Survivor Insurance; Reversionary Annuities.;

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