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, and are risk averse with same risk awareness level. Moreover, the agent’s quality is unknown and modeled as a filtering term in the problem, which is revealed as time passes by. The principal can not observe the agent’s real action, but can only recommend action levels to the agent. Hence, we have a moral hazard problem. In this setting, we give an explicit solution to the optimal contract problem.
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