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Threshold Life Tables and Their Applications

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  • Johnny Siu-Hang Li
  • Mary Hardy
  • Ken Seng Tan

Abstract

The rapid emergence of centenarians has highlighted the importance of survival probabilities at extreme ages and has motivated actuaries to look for alternative ways to close of life tables in place of assigning a death probability of 1 at an arbitrarily chosen age. Using the asymptotic results of modern extreme value theory, we propose a model, which we call the threshold life table, to extrapolate survival distributions to extreme ages and to determine the appropriate end point of a life table. By combining the threshold life table with the Lee-Carter model for stochastic mortality forecasting, we consider applications to the valuation of a life annuity portfolio and to the prediction of the highest attained age. We illustrate the theoretical results using U.S., Canadian, and Japanese mortality data.

Suggested Citation

  • Johnny Siu-Hang Li & Mary Hardy & Ken Seng Tan, 2008. "Threshold Life Tables and Their Applications," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(2), pages 99-115.
    • Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:99-115
    DOI: 10.1080/10920277.2008.10597505
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    Cited by:

    1. 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.
    2. 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.
    3. Jan Baldeaux & Eckhard Platen, 2013. "Liability Driven Investments under a Benchmark Based Approach," Research Paper Series 325, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Gbari, Kock Yed Ake Samuel & Poulain, Michel & Dal, Luc & Denuit, Michel, 2016. "Extreme value analysis of mortality at the oldest ages: a case study based on individual ages at death," LIDAM Discussion Papers ISBA 2016012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Li, J.S.H. & Ng, A.C.Y. & Chan, W.S., 2011. "Modeling old-age mortality risk for the populations of Australia and New Zealand: An extreme value approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1325-1333.
    6. Leunglung Chan & Eckhard Platen, 2016. "Pricing of long dated equity-linked life insurance contracts," Published Paper Series 2016-5, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    7. Anthony Medford, 2017. "Best-practice life expectancy: An extreme value approach," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 36(34), pages 989-1014.

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