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Love and death: A Freund model with frailty

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  • Christian Gouriéroux

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

  • Yang Lu

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

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 special copulas with continuous density. 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 jump in mortality intensity upon death of spouse (Freund model). The model is applied to the pricing of insurance products such as joint life policy, last survivor insurance, or contracts with reversionary annuities. A discussion of identification is also provided.

Suggested Citation

  • Christian Gouriéroux & Yang Lu, 2015. "Love and death: A Freund model with frailty," Post-Print hal-02419013, HAL.
    • Handle: RePEc:hal:journl:hal-02419013
    DOI: 10.1016/j.insmatheco.2015.03.016
    Note: View the original document on HAL open archive server: https://hal.science/hal-02419013
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    Cited by:

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    2. 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.
    3. Ayuso, Mercedes & Bravo, Jorge M. & Holzmann, Robert, 2021. "Getting life expectancy estimates right for pension policy: period versus cohort approach," Journal of Pension Economics and Finance, Cambridge University Press, vol. 20(2), pages 212-231, April.
    4. Christian Gourieroux & Yang Lu, 2013. "Long Term Care and Longevity," Working Papers 2013-16, Center for Research in Economics and Statistics.
    5. Kira Henshaw & Corina Constantinescu & Olivier Menoukeu Pamen, 2020. "Stochastic Mortality Modelling for Dependent Coupled Lives," Risks, MDPI, vol. 8(1), pages 1-28, February.
    6. Gerard J. van den Berg & Bettina Drepper, 2022. "A unique bond: Twin bereavement and lifespan associations of identical and fraternal twins," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(2), pages 677-698, April.
    7. Ying Jiao & Yahia Salhi & Shihua Wang, 2021. "Dynamic Bivariate Mortality Modelling," Working Papers hal-03244324, HAL.
    8. Joanna Dębicka & Stanisław Heilpern & Agnieszka Marciniuk, 2023. "Pricing Marriage Insurance with Mortality Dependence," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 15(1), pages 31-64, March.
    9. 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).
    10. Ying Jiao & Yahia Salhi & Shihua Wang, 2022. "Dynamic Bivariate Mortality Modelling," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 917-938, June.

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