  We develop a theory for valuing 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 apply our method to value life
annuities. One result of our paper is that the value of the life annuity is
{\it identical} to the upper good deal bound of Cochrane and Sa\'{a}-Requejo
(2000) and of Bj\"{o}rk and Slinko (2006) applied to our setting. A second
result of our paper is that the value per contract solves a {\it 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 (as in Blanchet-Scalliet, El Karoui, and
Martellini (2005)), and from this representation, one can interpret the
instantaneous Sharpe ratio as an annuity market's price of mortality risk.
