Dynamic programming approach to principal-agent problems

We consider a general formulation of the Principal-Agent problem with a lump-sum payment on a finite horizon. Our approach is the following: we first find the contract that is optimal among those for which the agent’s value process allows a dynamic programming representation and for which the agent’s optimal effort is straightforward to find. We then show that, under technical conditions, the optimization over the restricted family of contracts represents no loss of generality. Moreover, the principal’s problem can then be analyzed by the standard tools of control theory. Our proofs rely on the Backward Stochastic Differential Equations approach to non-Markovian stochastic control, and more specifically, on the recent extensions to the second order case.