The paper takes issue with the suggestion of Holmström and Milgrom (1987) that optimal incentive schemes in Brownian-motion models of principal-agent relations with effort costs depending on mean returns are linear in cumulative total returns. In such models, if actions are restricted to compact sets, boundary actions are optimal and typically can be implemented with lower risk premia than are implied by linear schemes. The paper characterizes optimal incentive schemes for discrete-time approximations as well as the Brownian-motion model itself. Solutions for discrete-time approximations - and the continuous-time limits of such solutions - always lie on the boundary.
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