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

Abstract

This paper studies the relation between discrete-time and continuous-time principal-agent models. We derive the continuous-time model as a limit of discrete-time 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.

Keywords: Principal-agent problems, linear incentive schemes, intertemporal incentive provision, Brownian motion

JEL Classification: C61, D82, J33