IDEAS home Printed from https://ideas.repec.org/a/spr/qualqt/v58y2024i6d10.1007_s11135-023-01786-6.html
   My bibliography  Save this article

Frailty-based Lee–Carter family of stochastic mortality models

Author

Listed:
  • Maria Carannante

    (University of Salerno)

  • Valeria D’Amato

    (University of Salerno)

  • Steven Haberman

    (City University of London)

  • Massimiliano Menzietti

    (University of Salerno)

Abstract

In the actuarial literature, frailty is defined to be the unobserved variable which encompasses all the factors affecting human mortality other than gender and age. Heterogeneity in individual frailty can play a significant role in population mortality dynamics. In the present paper, we identify the main latent factors that explain the frailty component, in order to clarify its role in mortality projections. We show, using longitudinal survey data, that frailty is mainly due to co-morbidities that impact on the process of deterioration in terms of the human body’s physiological capacity. Accordingly, we provide frailty-based stochastic models for projecting mortality based on the Lee–Carter family of models. We propose several versions that consider frailty both as an age-dependent and a time-dependent factor and also combining the interaction effects of age and time in comparison with the general level of mortality, and compare the resulting mortality projections using data from England.

Suggested Citation

  • Maria Carannante & Valeria D’Amato & Steven Haberman & Massimiliano Menzietti, 2024. "Frailty-based Lee–Carter family of stochastic mortality models," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(6), pages 5081-5105, December.
  • Handle: RePEc:spr:qualqt:v:58:y:2024:i:6:d:10.1007_s11135-023-01786-6
    DOI: 10.1007/s11135-023-01786-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11135-023-01786-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11135-023-01786-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2011. "Mortality density forecasts: An analysis of six stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 355-367, May.
    2. Mengyi Xu & Michael Sherris & Ramona Meyricke, 2019. "Systematic Mortality Improvement Trends and Mortality Heterogeneity: Insights from Individual-Level HRS Data," North American Actuarial Journal, Taylor & Francis Journals, vol. 23(2), pages 197-219, April.
    3. Annamaria Olivieri & Ermanno Pitacco, 2016. "Frailty and Risk Classification for Life Annuity Portfolios," Risks, MDPI, vol. 4(4), pages 1-23, October.
    4. Butt, Zoltan & Haberman, Steven, 2004. "Application of Frailty-Based Mortality Models Using Generalized Linear Models," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 175-197, May.
    5. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272.
    6. Geng Niu & Bertrand Melenberg, 2014. "Trends in Mortality Decrease and Economic Growth," Demography, Springer;Population Association of America (PAA), vol. 51(5), pages 1755-1773, October.
    7. W.J. Willemse & R. Kaas, 2007. "Rational reconstruction of frailty-based mortality models by a generalisation of Gompertz' law of mortality," DNB Working Papers 135, Netherlands Central Bank, Research Department.
    8. 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.
    9. Willemse, W.J. & Kaas, R., 2007. "Rational reconstruction of frailty-based mortality models by a generalisation of Gompertz' law of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 468-484, May.
    10. Meyricke, Ramona & Sherris, Michael, 2013. "The determinants of mortality heterogeneity and implications for pricing annuities," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 379-387.
    11. Strulik, Holger, 2015. "Frailty, mortality, and the demand for medical care," The Journal of the Economics of Ageing, Elsevier, vol. 6(C), pages 5-12.
    12. Su, Shu & Sherris, Michael, 2012. "Heterogeneity of Australian population mortality and implications for a viable life annuity market," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 322-332.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Annamaria Olivieri & Ermanno Pitacco, 2016. "Frailty and Risk Classification for Life Annuity Portfolios," Risks, MDPI, vol. 4(4), pages 1-23, October.
    2. Maria Carannante & Valeria D’amato & Steven Haberman & Massimiliano Menzietti, 2024. "Frailty-based mortality models and reserving for longevity risk," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 49(2), pages 320-339, April.
    3. Milevsky, Moshe A., 2020. "Calibrating Gompertz in reverse: What is your longevity-risk-adjusted global age?," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 147-161.
    4. Filipe Costa Souza & Wilton Bernardino & Silvio C. Patricio, 2024. "How life-table right-censoring affected the Brazilian social security factor: an application of the gamma-Gompertz-Makeham model," Journal of Population Research, Springer, vol. 41(3), pages 1-38, September.
    5. Bruszas, Sandy & Kaschützke, Barbara & Maurer, Raimond & Siegelin, Ivonne, 2018. "Unisex pricing of German participating life annuities—Boon or bane for customer and insurance company?," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 230-245.
    6. Jonas Šiaulys & Rokas Puišys, 2022. "Survival with Random Effect," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    7. Lydia Dutton & Athanasios A. Pantelous & Malgorzata Seklecka, 2020. "The impact of economic growth in mortality modelling for selected OECD countries," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(3), pages 533-550, April.
    8. Boonen, Tim J. & De Waegenaere, Anja & Norde, Henk, 2017. "Redistribution of longevity risk: The effect of heterogeneous mortality beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 175-188.
    9. de Jong, Piet & Tickle, Leonie & Xu, Jianhui, 2020. "A more meaningful parameterization of the Lee–Carter model," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 1-8.
    10. David Blake & Marco Morales & Enrico Biffis & Yijia Lin & Andreas Milidonis, 2017. "Special Edition: Longevity 10 – The Tenth International Longevity Risk and Capital Markets Solutions Conference," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(S1), pages 515-532, April.
    11. Katrien Antonio & Anastasios Bardoutsos & Wilbert Ouburg, 2015. "Bayesian Poisson log-bilinear models for mortality projections with multiple populations," BAFFI CAREFIN Working Papers 1505, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    12. Ana Debón & Steven Haberman & Francisco Montes & Edoardo Otranto, 2021. "Do Different Models Induce Changes in Mortality Indicators? That Is a Key Question for Extending the Lee-Carter Model," IJERPH, MDPI, vol. 18(4), pages 1-16, February.
    13. Alexander, Monica, 2018. "Deaths without denominators: using a matched dataset to study mortality patterns in the United States," SocArXiv q79ye, Center for Open Science.
    14. David Blake & Andrew Cairns & Guy Coughlan & Kevin Dowd & Richard MacMinn, 2013. "The New Life Market," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 501-558, September.
    15. Enrico Biffis & David Blake & Lorenzo Pitotti & Ariel Sun, 2016. "The Cost of Counterparty Risk and Collateralization in Longevity Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(2), pages 387-419, June.
    16. Rafal Chomik & John Piggott, 2016. "Australian Superannuation: The Current State of Play," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 49(4), pages 483-493, December.
    17. Kyran Cupido & Petar Jevtić & Tim J. Boonen, 2024. "Space, mortality, and economic growth," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(5), pages 1321-1337, August.
    18. D. Tabakova & E. Pitacco, 2021. "Heterogeneity and uncertainty in a multistate framework," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 117-139, June.
    19. Willemse, W.J. & Kaas, R., 2007. "Rational reconstruction of frailty-based mortality models by a generalisation of Gompertz' law of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 468-484, May.
    20. Lindholm, Mathias, 2017. "A note on the connection between some classical mortality laws and proportional frailty," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 76-82.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:qualqt:v:58:y:2024:i:6:d:10.1007_s11135-023-01786-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.