turkmath.org

We study an optimization problem related to the contract theory in continuous time with finite time horizon. The risk neutral principal hires a risk averse agent to manage a risky project with the aim of maximizing the cumulative output of the project. The cumulative output depends on the agents action, on an unknown productivity parameter as well as on a Brownian motion with constant volatility. The principal does not observe the actual effort of the agent but can only recommend effort to the agent and can see only the cumulative output, whereas the agent knows his actual effort as well as the cumulative output. This causes the moral hazard. The agent’s problem will be solved using the weak formulation of stochastic control, whereas the principal’s problem will be solved using the HJB approach.