A General Model for Continuous Time Principal-Agent Problem Under Hidden Action

In this paper, we study a general continuous-time Principal-Agent (PA) problem, where the agent privately makes effort and consumption decisions over time under a contract with payment schemes both in continuous time and in lump sums. In particular, we allow the continuous payment process to be a controlled diffusion, which is directly related to the pay-to-performance sensitivity (PPS) in the empirical literature. In solving the agent's problem, we propose a new sufficient condition that directly yields a solution to the agent's problem, without requiring a separate verification step for the solution obtained from the first-order approach. We also present an example which can be solved explicitly.