Abstract
We present here well-known examples and applications of continuous-time Principal–Agent models. The seminal work of Holmström and Milgrom (Econometrica 55:303–328,1987) is the first to use a continuous-time model, showing that doing that can, in fact, lead to simple, while realistic optimal contracts. In particular, if the principal and the agent maximize expected utility from terminal output value, and have non-separable cost of effort and exponential utilities, the optimal contract is linear in that value. With other utilities and separable cost of effort, the optimal contract is nonlinear in the terminal output value, obtained as a solution to a nonlinear equation that generalizes the first best Borch condition. In the case of the agent deriving utility from continuous contract payments on an infinite horizon, and if the principal is risk-neutral, the problem reduces to solving an ordinary differential equation for the principal’s expected utility process as a function of the agent’s expected utility process. That equation can then be solved numerically for various cases, including the case in which the agent can quit, or be replaced by another agent, or be trained and promoted. These cases are analyzed by studying the necessary conditions in terms of an FBSDE system for the agent’s problem, and, in Markovian models, by identifying sufficient conditions in terms of the HJB differential equation for the principal’s problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adrian, T., Westerfield, M.: Disagreement and learning in a dynamic contracting model. Rev. Financ. Stud. 22, 3839–3871 (2009)
Biais, B., Mariotti, T., Rochet, J.-C., Villeneuve, S.: Large risks, limited liability, and dynamic moral hazard. Econometrica 78, 73–118 (2010)
Cvitanić, J., Wan, X., Zhang, J.: Optimal contracts in continuous-time models. J. Appl. Math. Stoch. Anal. 2006, 1–27 (2006)
DeMarzo, P.M., Sannikov, Y.: Learning, termination and payout policy in dynamic incentive contracts. Working paper, Princeton University (2011)
Fong, K.G.: Evaluating skilled experts: optimal scoring rules for surgeons. Working paper, Stanford University (2009)
Giat, Y., Subramanian, A.: Dynamic contracting under imperfect public information and asymmetric beliefs. Working paper, Georgia State University (2009)
Giat, Y., Hackman, S.T., Subramanian, A.: Investment under uncertainty, heterogeneous beliefs and agency conflicts. Rev. Financ. Stud. 23(4), 1360–1404 (2011)
He, Z.: Optimal executive compensation when firm size follows geometric Brownian motion. Rev. Financ. Stud. 22, 859–892 (2009)
He, Z., Wei, B., Yu, J.: Permanent risk and dynamic incentives. Working paper, Baruch College (2010)
Holmström, B., Milgrom, P.: Aggregation and linearity in the provision of intertemporal incentives. Econometrica 55, 303–328 (1987)
Ou-Yang, H.: An equilibrium model of asset pricing and moral hazard. Rev. Financ. Stud. 18, 1219–1251 (2005)
Piskorski, T., Tchistyi, A.: Optimal mortgage design. Rev. Financ. Stud. 23, 3098–3140 (2010)
Prat, J., Jovanovic, B.: Dynamic incentive contracts under parameter uncertainty. Working paper, NYU (2010)
Sannikov, Y.: A continuous-time version of the principal-agent problem. Rev. Econ. Stud. 75, 957–984 (2008)
Sannikov, Y.: Contracts: the theory of dynamic principal-agent relationships and the continuous-time approach. Working paper, Princeton University (2012)
Zhang, Y.: Dynamic contracting with persistent shocks. J. Econ. Theory 144, 635–675 (2009)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Cvitanić, J., Zhang, J. (2013). Special Cases and Applications. In: Contract Theory in Continuous-Time Models. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14200-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-14200-0_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14199-7
Online ISBN: 978-3-642-14200-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)