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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

Topics: Equity-indexed annuity, indifference price, Hamilton-Jacobi- Bellman equation
Year: 2006
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