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Modelling and management of longevity risk: approximations to survivor functions and dynamic hedging. (English) Zbl 1230.91068
Summary: This paper looks at the development of dynamic hedging strategies for typical pension plan liabilities using longevity-linked hedging instruments. Progress in this area has been hindered by the lack of closed-form formulae for the valuation of mortality-linked liabilities and assets, and the consequent requirement for simulations within simulations. We propose the use of the probit function along with a Taylor expansion to approximate longevity-contingent values. This makes it possible to develop and implement computationally efficient, discrete-time delta hedging strategies using \(q\)-forwards as hedging instruments.
The methods are tested using the model proposed by A. J. G. Cairns, D. Blake and K. Dowd [“A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration”, J. Risk Insur. 73, No. 4, 687–718 (2006), http://www.jstor.org/stable/4138456]. We find that the probit approximations are generally very accurate, and that the discrete-time hedging strategy is very effective at reducing risk.

MSC:
91B30 Risk theory, insurance (MSC2010)
91G50 Corporate finance (dividends, real options, etc.)
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