The optimal solution to a principal-agent problem with unknown agent ability

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