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Published October 6, 2008 | Published
Journal Article Open

Principal-Agent Problems with Exit Options

Abstract

We consider the problem of when to deliver the contract payoff, in a continuous-time principal-agent setting, in which the agent's effort is unobservable. The principal can design contracts of a simple form that induce the agent to ask for the payoff at the time of the principal's choosing. The optimal time of payment depends on the agent's and the principal's outside options. We develop a theory for general utility functions, while with CARA utilities we are able to specify conditions under which the optimal payment time is not random. However, in general, the optimal payment time is typically random. One illustrative application is the case when the agent can be fired, after having been paid a severance payment, and then replaced by another agent. The methodology we use is the stochastic maximum principle and its link to Forward-Backward Stochastic Differential Equations.

Additional Information

© 2008 The Berkeley Electronic Press. Submitted: April 13, 2008. Accepted: August 26, 2008. Published: October 6, 2008. An earlier version of this paper was titled "Optimal Contracting with Random Time of Payment and Outside Options." We are very grateful to the editor and the anonymous referees for helpful suggestions that significantly improved the exposition of the paper. We are solely responsible for any remaining errors, and the opinions, findings and conclusions or suggestions in this article do not necessarily reflect anyone's opinions but the authors'. Research supported in part by NSF grants DMS 04-03575, DMS 06-31298, DMS 06-31366, the grant DAG 05/06.BM28 from HKUST, and through the Programme "GUEST" of the National Foundation For Science, Higher Education and Technological Development of the Republic of Croatia.

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August 22, 2023
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