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

Abstract

We consider a continuous-time principal-agent model on a finite time horizon, where we look for the existence of an optimal contract that both parties agreed on. Contrary to the mainstream, where the principal is modeled 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 is modeled as a filtering term in the problem, which is revealed as time passes. The principal cannot 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.