Pricing equity-linked pure endowments via the principle of equivalent utility

We consider a pure endowment contract whose life contingent payout is linked to the performance of a risky stock or index. Because of the additional mortality risk, the market is incomplete; thus, a fundamental assumption of the Black–Scholes theory is violated. We price this contract via the principle of equivalent utility and demonstrate that, under the assumption of exponential utility, the indifference price solves a nonlinear Black–Scholes equation; the nonlinear term reflects the mortality risk and exponential risk preferences in our model. We discuss qualitative and quantitative properties of the premium, including analytical upper and lower bounds.