THE OPTIMAL SOLUTION TO A PRINCIPAL-AGENT PROBLEM WITH UNKNOWN AGENT ABILITY

摘要

We investigate a principal-agent model featured with unknownagent ability. Under the exponential utilities, the necessary and sufficient conditionsof the incentive contract are derived by utilizing the martingale andvariational methods, and the solutions of the optimal contracts are obtainedby using the stochastic maximum principle. The ability uncertainty reducesthe 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 forbelief manipulation, and incentive provision will become easier. Namely, asthe contractual time tends to infinity (long-term), the agent ability is revealedcompletely, the ability uncertainty disappears, and the optimal contracts underknown and unknown ability become identical.