A Continuous-Time Version of the Principal-Agent Problem
This paper describes a new continuous-time principal-agent model, in which the output is a diffusion process with drift determined by the agent’s unobserved effort. The risk-averse agent receives consumption continuously. The optimal contract, based on the agent’s continuation value as a state variable, is computed by a new method using a differential equation. During employment, the output path stochastically drives the agent’s continuation value until it reaches a point that triggers retirement, quitting, replacement, or promotion. The paper explores how the dynamics of the agent’s wages and effort, as well as the optimal mix of short-term and long-term incentives, depend on the contractual environment.