We investigate a principal-agent model featured with unknown agent ability. Under the exponential utilities, the necessary and sufficient conditions of the incentive contract are derived by utilizing the martingale and variational methods, and the solutions of the optimal contracts are obtained by using the stochastic maximum principle. The ability uncertainty reduces the principal's ability of incentive provision. It is shown that as time goes by, the information about the ability accumulates, giving the agent less space for belief manipulation, and incentive provision will become easier. Namely, as the contractual time tends to infinity (long-term), the agent ability is revealed completely, the ability uncertainty disappears, and the optimal contracts under known and unknown ability become identical.

中文翻译：

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代理能力未知的委托代理问题的最优解

我们研究了具有未知代理能力的委托代理模型。在指数效用下，利用鞅和变分方法推导出激励契约的充要条件，利用随机最大值原理得到最优契约的解。能力的不确定性降低了委托人提供激励的能力。结果表明，随着时间的推移，能力的信息积累，给智能体更少的信念操纵空间，激励提供将变得更加容易。即随着合同时间趋于无穷大（长期），代理能力完全展现，能力不确定性消失，已知和未知能力下的最优合同变得相同。