Mathematics and Financial Economics

, Volume 1, Issue 1, pp 21–55 | Cite as

Optimal compensation with adverse selection and dynamic actions

  • Jakša Cvitanić
  • Jianfeng Zhang
Original Article


We consider continuous-time models in which the agent is paid at the end of the time horizon by the principal, who does not know the agent’s type. The agent dynamically affects either the drift of the underlying output process, or its volatility. The principal’s problem reduces to a calculus of variation problem for the agent’s level of utility. The optimal ratio of marginal utilities is random, via dependence on the underlying output process. When the agent affects the drift only, in the risk- neutral case lower volatility corresponds to the more incentive optimal contract for the smaller range of agents who get rent above the reservation utility. If only the volatility is affected, the optimal contract is necessarily non-incentive, unlike in the first-best case. We also suggest a procedure for finding simple and reasonable contracts, which, however, are not necessarily optimal.


Adverse selection Moral hazard Principal-agent problems Continuous-time models Contracts Managers compensation 

JEL Classification

C61 C73 D82 J33 M52 

Mathematics Subject Classification (2000)

91B28 93E20 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Caltech, Humanities and Social SciencesPasadenaUSA
  2. 2.USC Department of MathematicsLos AngelesUSA

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