The Principal-Agent Problem; A Stochastic Maximum Principle Approach
  We study a general class of Principal-Agent problems in continuous time under hidden action. By formulating the model as a coupled stochastic optimal control problem we are able to find a set of necessary conditions characterizing optimal contracts, using the stochastic maximum principle. An example is carried out to illustrate the proposed approach to the Principal-Agent problem under linear stochastic dynamics with a quadratic performance function. 
Boualem Djehiche, Peter Helgesson
math.OC