Finance and Stochastics

, Volume 22, Issue 1, pp 1–37 | Cite as

Dynamic programming approach to principal–agent problems

  • Jakša CvitanićEmail author
  • Dylan Possamaï
  • Nizar Touzi


We consider a general formulation of the principal–agent problem with a lump-sum payment on a finite horizon, providing a systematic method for solving such problems. Our approach is the following. We first find the contract that is optimal among those for which the agent’s value process allows a dynamic programming representation, in which case the agent’s optimal effort is straightforward to find. We then show that the optimization over this restricted family of contracts represents no loss of generality. As a consequence, we have reduced a non-zero-sum stochastic differential game to a stochastic control problem which may be addressed by standard tools of control theory. Our proofs rely on the backward stochastic differential equations approach to non-Markovian stochastic control, and more specifically on the recent extensions to the second order case.


Stochastic control of non-Markov systems Hamilton–Jacobi–Bellman equations Second order backward SDEs Principal–agent problem Contract theory 

Mathematics Subject Classification (2010)

91B40 93E20 

JEL Classification

C61 C73 D82 J33 M52 


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Jakša Cvitanić
    • 1
    Email author
  • Dylan Possamaï
    • 2
  • Nizar Touzi
    • 3
  1. 1.CaltechHumanities and Social SciencesPasadenaUSA
  2. 2.PSL Research University, CNRS, CEREMADEUniversité Paris–DauphineParisFrance
  3. 3.CMAPÉcole PolytechniquePalaiseauFrance

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