Continuous-time Principal-Agent Problem in a Linear Partially Observed System

Résumé

In this presentation, we are going to consider the Principal-Agent problem in a linear partially observed system. The non-observable part of the system is assumed not observable by the Principal or the Agent. Firstly, we shall demonstrate that the solvability of the Agent’s optimization problem can be reduced to the solvability of a system of strongly coupled FBSDEs using variational calculus in the weak formulation and we shall give a corresponding sufficient condition of the problem as well. Secondly, we will compute the optimal contract for the Principal’s problem in the risk-neutral case. In the end, we will also give a numerical scheme to determine the optimal value for the Principal in the relaxed formulation.