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Time-consistent longevity hedging with long-range dependence

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  • Wang, Ling
  • Wong, Hoi Ying

Abstract

Longevity securitization enables insurers to manage longevity or mortality risk in the life market. Recent empirical studies identify long-range dependence (LRD) in mortality rates using life tables, which casts doubt on the adequacy of Markovian models for actuarial pricing and risk management. This paper derives the first time-consistent mean–variance longevity hedging strategy for insurers using a stochastic mortality model with LRD. We adopt the open-loop equilibrium control framework and derive an analytical solution to the hedging strategy. Our numerical examples show the relevance of LRD to longevity hedging and the cost of ignoring it.

Suggested Citation

  • Wang, Ling & Wong, Hoi Ying, 2021. "Time-consistent longevity hedging with long-range dependence," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 25-41.
    • Handle: RePEc:eee:insuma:v:99:y:2021:i:c:p:25-41
    DOI: 10.1016/j.insmatheco.2021.03.004
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    References listed on IDEAS

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    1. Tat Wing Wong & Mei Choi Chiu & Hoi Ying Wong, 2017. "Managing Mortality Risk With Longevity Bonds When Mortality Rates Are Cointegrated," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 987-1023, September.
    2. David Blake & Andrew Cairns & Kevin Dowd & Richard MacMinn, 2006. "Longevity Bonds: Financial Engineering, Valuation, and Hedging," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 647-672, December.
    3. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2012. "Time-Inconsistent Stochastic Linear--Quadratic Control," Post-Print hal-00691816, HAL.
    4. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    5. Ngai, Andrew & Sherris, Michael, 2011. "Longevity risk management for life and variable annuities: The effectiveness of static hedging using longevity bonds and derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 100-114, July.
    6. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    7. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    8. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    9. Zhongyang Sun & Xianping Guo, 2019. "Equilibrium for a Time-Inconsistent Stochastic Linear–Quadratic Control System with Jumps and Its Application to the Mean-Variance Problem," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 383-410, May.
    10. Yan, Tingjin & Wong, Hoi Ying, 2020. "Open-loop equilibrium reinsurance-investment strategy under mean–variance criterion with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 105-119.
    11. Bingyan Han & Hoi Ying Wong, 2019. "Mean-variance portfolio selection under Volterra Heston model," Papers 1904.12442, arXiv.org, revised Jan 2020.
    12. David Blake & Richard MacMinn, 2020. "Longevity Risk and Capital Markets: The 2016–2017 Update," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(S1), pages 1-6, December.
    13. Wang, Ling & Chiu, Mei Choi & Wong, Hoi Ying, 2021. "Volterra mortality model: Actuarial valuation and risk management with long-range dependence," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 1-14.
    14. Menoncin, Francesco, 2008. "The role of longevity bonds in optimal portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 343-358, February.
    15. Wong, Tat Wing & Chiu, Mei Choi & Wong, Hoi Ying, 2014. "Time-consistent mean–variance hedging of longevity risk: Effect of cointegration," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 56-67.
    16. Yan, Hongxuan & Peters, Gareth W. & Chan, Jennifer, 2021. "Mortality models incorporating long memory for life table estimation: a comprehensive analysis," Annals of Actuarial Science, Cambridge University Press, vol. 15(3), pages 567-604, November.
    17. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2017. "Time-Inconsistent Stochastic Linear--Quadratic Control: Characterization and Uniqueness of Equilibrium," Post-Print hal-01139343, HAL.
    18. David Blake & Richard MacMinn & Jason Chenghsien Tsai & Jennifer Wang, 2020. "Longevity Risk and Capital Markets: The 2017–2018 Update," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(S1), pages 280-308, December.
    19. Tomas Björk & Mariana Khapko & Agatha Murgoci, 2017. "On time-inconsistent stochastic control in continuous time," Finance and Stochastics, Springer, vol. 21(2), pages 331-360, April.
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    Cited by:

    1. Ling Wang & Mei Choi Chiu & Hoi Ying Wong, 2021. "Time-consistent mean-variance reinsurance-investment problem with long-range dependent mortality rate," Papers 2112.06602, arXiv.org.
    2. Zhou, Hongjuan & Zhou, Kenneth Q. & Li, Xianping, 2022. "Stochastic mortality dynamics driven by mixed fractional Brownian motion," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 218-238.

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