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Dynamic programming approach to principal-agent problems

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  • Jakv{s}a Cvitani'c
  • Dylan Possamai
  • Nizar Touzi

Abstract

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, for which the agent's optimal effort is straightforward to find. We then show that the optimization over the restricted family of contracts represents no loss of generality. As a consequence, we have reduced this non-zero sum stochastic differential game to a stochastic control problem which may be addressed by the 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.

Suggested Citation

  • Jakv{s}a Cvitani'c & Dylan Possamai & Nizar Touzi, 2015. "Dynamic programming approach to principal-agent problems," Papers 1510.07111, arXiv.org, revised Jan 2017.
    • Handle: RePEc:arx:papers:1510.07111
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    References listed on IDEAS

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    1. Patrick Bolton & Mathias Dewatripont, 2005. "Contract Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262025760, April.
    2. Muller, Holger M., 1998. "The First-Best Sharing Rule in the Continuous-Time Principal-Agent Problem with Exponential Utility," Journal of Economic Theory, Elsevier, vol. 79(2), pages 276-280, April.
    3. repec:dau:papers:123456789/13348 is not listed on IDEAS
    4. Martin F. Hellwig & Klaus M. Schmidt, 2002. "Discrete-Time Approximations of the Holmstrom-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Econometrica, Econometric Society, vol. 70(6), pages 2225-2264, November.
    5. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    6. Schattler Heinz & Sung Jaeyoung, 1993. "The First-Order Approach to the Continuous-Time Principal-Agent Problem with Exponential Utility," Journal of Economic Theory, Elsevier, vol. 61(2), pages 331-371, December.
    7. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    8. Karandikar, Rajeeva L., 1995. "On pathwise stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 11-18, May.
    9. Schattler, Heinz & Sung, Jaeyoung, 1997. "On optimal sharing rules in discrete-and continuous-time principal-agent problems with exponential utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 551-574.
    10. Sung, Jaeyoung, 1997. "Corporate Insurance and Managerial Incentives," Journal of Economic Theory, Elsevier, vol. 74(2), pages 297-332, June.
    11. Jaeyoung Sung, 1995. "Linearity with Project Selection and Controllable Diffusion Rate in Continuous-Time Principal-Agent Problems," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 720-743, Winter.
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    Citations

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    Cited by:

    1. Thibaut Mastrolia, 2017. "Moral hazard in welfare economics: on the advantage of Planner's advices to manage employees' actions," Working Papers hal-01504473, HAL.
    2. Cvitanić, Jakša & Xing, Hao, 2018. "Asset pricing under optimal contracts," Journal of Economic Theory, Elsevier, vol. 173(C), pages 142-180.
    3. Thibaut Mastrolia & Dylan Possamai, 2015. "Moral hazard under ambiguity," Papers 1511.03616, arXiv.org, revised Oct 2016.
    4. Dylan Possamai & Xiaolu Tan & Chao Zhou, 2015. "Stochastic control for a class of nonlinear kernels and applications," Papers 1510.08439, arXiv.org, revised Jul 2017.
    5. Thibaut Mastrolia, 2017. "Moral hazard in welfare economics: on the advantage of Planner's advices to manage employees' actions," Papers 1706.01254, arXiv.org.
    6. Rene Carmona, 2020. "Applications of Mean Field Games in Financial Engineering and Economic Theory," Papers 2012.05237, arXiv.org.

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