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Dynamic programming approach to principal–agent problems

Author

Listed:
  • Jakša Cvitanić

    (Humanities and Social Sciences)

  • Dylan Possamaï

    (Université Paris–Dauphine)

  • Nizar Touzi

    (École Polytechnique)

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, 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.

Suggested Citation

  • Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2018. "Dynamic programming approach to principal–agent problems," Finance and Stochastics, Springer, vol. 22(1), pages 1-37, January.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:1:d:10.1007_s00780-017-0344-4
    DOI: 10.1007/s00780-017-0344-4
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    References listed on IDEAS

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    More about this item

    Keywords

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

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • J33 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Compensation Packages; Payment Methods
    • M52 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics - - - Compensation and Compensation Methods and Their Effects

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