  We develop a pricing rule for life insurance under stochastic mortality in an
incomplete market by assuming that the insurance company requires compensation
for its risk in the form of a pre-specified instantaneous Sharpe ratio. Our
valuation formula satisfies a number of desirable properties, many of which it
shares with the standard deviation premium principle. The major result of the
paper is that the price per contract solves a linear partial differential
equation as the number of contracts approaches infinity. One can interpret the
limiting price as an expectation with respect to an equivalent martingale
measure. Another important result is that if the hazard rate is stochastic,
then the risk-adjusted premium is greater than the net premium, even as the
number of contracts approaches infinity. We present a numerical example to
illustrate our results, along with the corresponding algorithms.
