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We consider a continuous time Principal-Agent model on a finite time horizon,where we look for the existence of an optimal contract both parties agreed on.Contrary to the main stream, where the principal is modelled as risk-neutral,we assume that both the principal and the agent have exponential utility, andare risk averse with same risk awareness level. Moreover, the agent's qualityis unknown and modelled as a filtering term in the problem, which is revealedas time passes by. The principal can not observe the agent's real action, butcan only recommend action levels to the agent. Hence, we have a \textit{moralhazard} problem. In this setting, we give an explicit solution to the optimalcontract problem.

Dynamic optimal contract under parameter uncertainty with risk averse agent and principal