The Role of Boundary Solutions in Principal-Agent Problems with Effort Costs Depending on Mean Returns

Martin Hellwig

No 01-51, Sonderforschungsbereich 504 Publications from Sonderforschungsbereich 504, Universität Mannheim, Sonderforschungsbereich 504, University of Mannheim

Abstract: 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.

Pages: 37 pages
Date: 2001-08-06
Note: This paper owes a lot to Klaus Schmidt and Paul Milgrom. Klaus Schmidt made the observation that in the static agency model with effort cost depending only on mean returns, the principal prefers the action that involves the lowest risk premium and therefore will implement a boundary action. Paul Milgrom suggested that this reasoning for the static model must have a counterpart in the continuous-time model. I am very grateful to both. I am also grateful for helpful remarks from Drew Fudenberg and Bengt Holmström and for financial support from the Taussig Chair at Harvard University and from the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 504 at the University of Mannheim.
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