A Continuous-Time Version of the Principal-Agent

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. An 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 hits a low retirement point or a high retirement point. Unlike in related discrete-time models, one can use calculus to derive comparative statics and evaluate inefficiency