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Financial Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Pricing Pure Endowments

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  • Moshe A. Milevsky
  • S. David Promislow
  • Virginia R. Young
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    Abstract

    We develop a theory for pricing non-diversifiable mortality risk in an incomplete market. We do this by assuming that the company issuing a mortality-contingent claim requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. We prove that our ensuing valuation formula satisfies a number of desirable properties. For example, we show that it is subadditive in the number of contracts sold. A key result is that if the hazard rate is stochastic, then the risk-adjusted survival probability is greater than the physical survival probability, even as the number of contracts approaches infinity.

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    File URL: http://arxiv.org/pdf/0705.1302
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    Paper provided by arXiv.org in its series Papers with number 0705.1302.

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    Date of creation: May 2007
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    Handle: RePEc:arx:papers:0705.1302

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    1. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    2. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Martellini, Lionel, 2005. "Dynamic asset pricing theory with uncertain time-horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1737-1764, October.
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