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Mortality modelling with Lévy processes

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  • Hainaut, Donatien
  • Devolder, Pierre

Abstract

This paper addresses the modelling of human mortality by the aid of doubly stochastic processes with an intensity driven by a positive Lévy process. We focus on intensities having a mean reverting stochastic component. Furthermore, driving Lévy processes are pure jump processes belonging to the class of [alpha]-stable subordinators. In this setting, expressions of survival probabilities are inferred, the pricing is discussed and numerical applications to actuarial valuations are proposed.

Suggested Citation

  • Hainaut, Donatien & Devolder, Pierre, 2008. "Mortality modelling with Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 409-418, February.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:409-418
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    Cited by:

    1. Areski Cousin & Ibrahima Niang, 2014. "On the Range of Admissible Term-Structures," Working Papers hal-00968943, HAL.
    2. Shen, Yang & Siu, Tak Kuen, 2013. "Longevity bond pricing under stochastic interest rate and mortality with regime-switching," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 114-123.
    3. Raj Kumari Bahl & Sotirios Sabanis, 2016. "Model-Independent Price Bounds for Catastrophic Mortality Bonds," Papers 1607.07108, arXiv.org, revised Dec 2020.
    4. Kalloniatis, Alexander C. & McLennan-Smith, Timothy A. & Roberts, Dale O., 2020. "Modelling distributed decision-making in Command and Control using stochastic network synchronisation," European Journal of Operational Research, Elsevier, vol. 284(2), pages 588-603.
    5. Bahl, Raj Kumari & Sabanis, Sotirios, 2021. "Model-independent price bounds for Catastrophic Mortality Bonds," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 276-291.
    6. Stefan Tappe & Stefan Weber, 2014. "Stochastic mortality models: an infinite-dimensional approach," Finance and Stochastics, Springer, vol. 18(1), pages 209-248, January.
    7. Ahmadi, Seyed Saeed & Gaillardetz, Patrice, 2015. "Modeling mortality and pricing life annuities with Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 337-350.
    8. Huang, Yu-Lieh & Tsai, Jeffrey Tzuhao & Yang, Sharon S. & Cheng, Hung-Wen, 2014. "Price bounds of mortality-linked security in incomplete insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 30-39.
    9. Chou-Wen Wang & Hong-Chih Huang & I-Chien Liu, 2013. "Mortality Modeling With Non-Gaussian Innovations and Applications to the Valuation of Longevity Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 775-798, September.
    10. Liu, Yanxin & Li, Johnny Siu-Hang, 2015. "The age pattern of transitory mortality jumps and its impact on the pricing of catastrophic mortality bonds," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 135-150.
    11. Areski Cousin & Ibrahima Niang, 2014. "On the range of admissible term-structures," Papers 1404.0340, arXiv.org.
    12. 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.
    13. Lin, Tzuling & Tzeng, Larry Y., 2010. "An additive stochastic model of mortality rates: An application to longevity risk in reserve evaluation," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 423-435, April.

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