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Time-consistent mean–variance hedging of longevity risk: Effect of cointegration

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  • Wong, Tat Wing
  • Chiu, Mei Choi
  • Wong, Hoi Ying

Abstract

This paper investigates the time-consistent dynamic mean–variance hedging of longevity risk with a longevity security contingent on a mortality index or the national mortality. Using an HJB framework, we solve the hedging problem in which insurance liabilities follow a doubly stochastic Poisson process with an intensity rate that is correlated and cointegrated to the index mortality rate. The derived closed-form optimal hedging policy articulates the important role of cointegration in longevity hedging. We show numerically that a time-consistent hedging policy is a smoother function in time when compared with its time-inconsistent counterpart.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:insuma:v:56:y:2014:i:c:p:56-67 DOI: 10.1016/j.insmatheco.2014.03.001
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    Cited by:

    1. Leng, Xuan & Peng, Liang, 2016. "Inference pitfalls in Lee–Carter model for forecasting mortality," Insurance: Mathematics and Economics, Elsevier, pages 58-65.
    2. Peter Jevtic & Luca Regis, 2016. "A continuous-time stochastic model for the mortality surface of multiple populations," Working Papers 03/2016, IMT Institute for Advanced Studies Lucca, revised Jul 2016.
    3. Kwok, Kai Yin & Chiu, Mei Choi & Wong, Hoi Ying, 2016. "Demand for longevity securities under relative performance concerns: Stochastic differential games with cointegration," Insurance: Mathematics and Economics, Elsevier, pages 353-366.
    4. Dong, Fangyuan & Wong, Hoi Ying, 2015. "Longevity bond pricing under the threshold CIR model," Finance Research Letters, Elsevier, vol. 15(C), pages 195-207.
    5. Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2016. "Semiparametric error-correction models for cointegration with trends: Pseudo-Gaussian and optimal rank-based tests of the cointegration rank," Journal of Econometrics, Elsevier, vol. 190(1), pages 46-61.
    6. Clemente De Rosa & Elisa Luciano & Luca Regis, 2015. "Basis risk in static versus dynamic longevity-risk hedging," Carlo Alberto Notebooks 425, Collegio Carlo Alberto, revised Oct 2015.
    7. Helena Chuliá & Montserrat Guillén & Jorge M. Uribe, 2015. "Mortality and Longevity Risks in the United Kingdom: Dynamic Factor Models and Copula-Functions," Working Papers 2015-03, Universitat de Barcelona, UB Riskcenter.
    8. repec:eee:insuma:v:75:y:2017:i:c:p:1-15 is not listed on IDEAS

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