Journal
JOURNAL OF ECONOMIC DYNAMICS & CONTROL
Volume 33, Issue 3, Pages 676-691Publisher
ELSEVIER
DOI: 10.1016/j.jedc.2008.09.004
Keywords
Stochastic mortality; Pricing; Annuities; Sharpe ratio; Non-linear partial differential equations; Market price of risk; Equivalent martingale measures
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We 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 Saa-Requejo [2000. Beyond arbitrage: good deal asset price bounds in incomplete markets. Journal of Political Economy 108, 79-119] and of Bjork 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. (C) 2008 Elsevier B.V. All rights reserved.
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