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Extreme Value Analysis of Mortality at the Oldest Ages: A Case Study Based on Individual Ages at Death

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  • Samuel Gbari
  • Michel Poulain
  • Luc Dal
  • Michel Denuit

Abstract

In this article, the force of mortality at the oldest ages is studied using the statistical tools from extreme value theory. A unique data basis recording all individual ages at death above 95 for extinct cohorts born in Belgium between 1886 and 1904 is used to illustrate the relevance of the proposed approach. No leveling off in the force of mortality at the oldest ages is found, and the analysis supports the existence of an upper limit to human lifetime for these cohorts. Therefore, assuming that the force of mortality becomes ultimately constant, that is, that the remaining lifetime tends to the Negative Exponential distribution as the attained age grows is a conservative strategy for managing life annuities.

Suggested Citation

  • Samuel Gbari & Michel Poulain & Luc Dal & Michel Denuit, 2017. "Extreme Value Analysis of Mortality at the Oldest Ages: A Case Study Based on Individual Ages at Death," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(3), pages 397-416, July.
    • Handle: RePEc:taf:uaajxx:v:21:y:2017:i:3:p:397-416
    DOI: 10.1080/10920277.2017.1301260
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    Cited by:

    1. Anthony Medford & James W. Vaupel, 2020. "Extremes are not normal: a reminder to demographers," Journal of Population Research, Springer, vol. 37(1), pages 91-106, March.
    2. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    3. Jesson J. Einmahl & John H. J. Einmahl & Laurens de Haan, 2019. "Limits to Human Life Span Through Extreme Value Theory," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1075-1080, July.
    4. Huang, Fei & Maller, Ross & Ning, Xu, 2020. "Modelling life tables with advanced ages: An extreme value theory approach," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 95-115.
    5. Jackie Li & Jia Liu, 2020. "A modified extreme value perspective on best-performance life expectancy," Journal of Population Research, Springer, vol. 37(4), pages 345-375, December.
    6. Anthony Medford & James W Vaupel, 2019. "Human lifespan records are not remarkable but their durations are," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-9, March.
    7. Linh Hoang Khanh Dang & Carlo Giovanni Camarda & France Meslé & Nadine Ouellette & Jean-Marie Robine & Jacques Vallin, 2023. "The question of the human mortality plateau: Contrasting insights by longevity pioneers," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 48(11), pages 321-338.

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