Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities
AbstractWe develop a theory for valuing non-diversifiable mortality risk in an incomplete market 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 apply our method to value life annuities. One result of our paper is that the value of the life annuity is identical to the upper good deal bound of Cochrane and Saá-Requejo [2000. Beyond arbitrage: good deal asset price bounds in incomplete markets. Journal of Political Economy 108, 79-119] and of Björk and Slinko [2006. Towards a general theory of good deal bounds. Review of Finance 10, 221-260] applied to our setting. A second result of our paper is that the value per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can represent the limiting value as an expectation with respect to an equivalent martingale measure, and from this representation, one can interpret the instantaneous Sharpe ratio as an annuity market's price of mortality risk.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Dynamics and Control.
Volume (Year): 33 (2009)
Issue (Month): 3 (March)
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Web page: http://www.elsevier.com/locate/jedc
Stochastic mortality Pricing Annuities Sharpe ratio Non-linear partial differential equations Market price of risk Equivalent martingale measures;
Other versions of this item:
- Erhan Bayraktar & Moshe Milevsky & David Promislow & Virginia Young, 2008. "Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities," Papers 0802.3250, arXiv.org.
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