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

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 proc...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2014-05, Vol.56, p.56-67
Main Authors: Wong, Tat Wing, Chiu, Mei Choi, Wong, Hoi Ying
Format: Article
Language:English
Subjects:
Basis risk
Cointegration
Hedging
Longevity risk
Mortality
Security
Stochastic mortality
Stochastic processes
Time
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Summary: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.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2014.03.001