Discrete-Time Approximations of the Holmström-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision

This paper studies the relation between discrete-time and
continuoustime principal-agent models. We derive the
continuous-time model as a limit of discretetime models with ever
shorter periods and show that optimal incentive schemes in the
discrete-time models approximate the optimal incentive scheme in
the continuous model, which is linear in accounts. Under the
additional assumption that the principal observes only cumulative
total profits at the end and the agent can destroy profits
unnoticed, an incentive scheme that is linear in total profits is
shown to be approximately optimal in the discrete-time model when
the length of the period is small.