Mathematical Theory for General Moral Hazard Problems
 Jakša Cvitanić,
 Jianfeng Zhang
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Abstract
This chapter describes a general theory of optimal contracting with hidden or noncontractable actions in continuoustime, developed by applying the stochastic maximum principle. The main modeling difference with respect to the full information case is that we will now assume that the agent controls the distribution of the output process with his effort. Mathematically, this is modeled using the socalled “weak formulation” and “weak solutions” of the underlying SDEs. Necessary and sufficient conditions are derived in terms of the socalled adjoint processes and corresponding ForwardBackward SDEs. These processes typically include the output process, the agent’s expected utility process, the principal’s expected utility process, and the ratio of marginal utilities process.
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 Sannikov, Y.: Contracts: the theory of dynamic principalagent relationships and the continuoustime approach. Working paper, Princeton University (2012)
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 Williams, N.: On dynamic principalagent problems in continuous time. Working paper, University of WisconsinMadison (2009)
 Title
 Mathematical Theory for General Moral Hazard Problems
 Book Title
 Contract Theory in ContinuousTime Models
 Pages
 pp 4784
 Copyright
 2013
 DOI
 10.1007/9783642142000_5
 Print ISBN
 9783642141997
 Online ISBN
 9783642142000
 Series Title
 Springer Finance
 Series ISSN
 16160533
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Authors

 Jakša Cvitanić ^{(3)} ^{(4)}
 Jianfeng Zhang ^{(5)}
 Author Affiliations

 3. Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, CA, USA
 4. EDHEC Business School, Nice, France
 5. Department of Mathematics, University of Southern California, Los Angeles, CA, USA
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