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Love and Death : A Freund Model with Frailty

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  • Christian Gouriéroux

    () (Crest, University of Toronto)

  • Yang Lu

    () (SCOR and Crest)

Abstract

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

    as
    1. 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.
    2. repec:aph:ajpbhl:10.2105/ajph.2007.119271_2 is not listed on IDEAS
    3. Gouriéroux, C. & Monfort, A. & Renne, J.P., 2014. "Pricing default events: Surprise, exogeneity and contagion," Journal of Econometrics, Elsevier, vol. 182(2), pages 397-411.
    4. 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(02), pages 236-257, September.
    5. 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.
    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. Jaap H. Abbring & Gerard J. van den Berg, 2003. "The identifiability of the mixed proportional hazards competing risks model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 701-710.
    8. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515 World Scientific Publishing Co. Pte. Ltd..
    9. Jaap H. Abbring & Gerard J. van den Berg, 2003. "The Nonparametric Identification of Treatment Effects in Duration Models," Econometrica, Econometric Society, vol. 71(5), pages 1491-1517, September.
    10. 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. repec:eee:insuma:v:78:y:2018:i:c:p:157-173 is not listed on IDEAS
    2. Christian Gourieroux & Yang Lu, 2013. "Long Term Care and Longevity," Working Papers 2013-16, Center for Research in Economics and Statistics.
    3. Ayuso, Mercedes & Bravo, Jorge Miguel & Holzmann, Robert, 2018. "Getting Life Expectancy Estimates Right for Pension Policy: Period versus Cohort Approach," IZA Discussion Papers 11512, Institute for the Study of Labor (IZA).
    4. 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 for the Study of Labor (IZA).

    More about this item

    Keywords

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

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