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A two-dimensional control problem arising from dynamic contracting theory

Author

Listed:
  • Jean-Paul Décamps

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • Stéphane Villeneuve

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

Abstract

We study a dynamic corporate finance contracting model in which the firm's profitability fluctuates and is impacted by the unobservable managerial effort. Thereby, we introduce in an agency framework the issue of strategic liquidation. We show that the principal's problem takes the form of a two-dimensional fully degenerate Markov control problem. We prove regularity properties of the value function and derive explicitly the optimal contract that implements full effort. Our regularity results appear in some recent studies, but with heuristic proofs that do not clarify the importance of the regularity of the value function at the boundaries

Suggested Citation

  • Jean-Paul Décamps & Stéphane Villeneuve, 2019. "A two-dimensional control problem arising from dynamic contracting theory," Post-Print halshs-02282092, HAL.
    • Handle: RePEc:hal:journl:halshs-02282092
    DOI: 10.1007/s00780-018-0376-4
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    References listed on IDEAS

    as
    1. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
    2. Bruno Biais & Thomas Mariotti & Guillaume Plantin & Jean-Charles Rochet, 2007. "Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 345-390.
    3. John Y. Zhu, 2013. "Optimal Contracts with Shirking," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(2), pages 812-839.
    4. Strulovici, Bruno & Szydlowski, Martin, 2015. "On the smoothness of value functions and the existence of optimal strategies in diffusion models," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 1016-1055.
    5. Bruno Strulovici & Martin Szydlowski, 2012. "On the Smoothness of Value Functions," Discussion Papers 1542, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    7. 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.
    8. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
    9. 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.
    10. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    11. PETER M. DeMARZO & YULIY SANNIKOV, 2006. "Optimal Security Design and Dynamic Capital Structure in a Continuous‐Time Agency Model," Journal of Finance, American Finance Association, vol. 61(6), pages 2681-2724, December.
    12. Zhiguo He, 2009. "Optimal Executive Compensation when Firm Size Follows Geometric Brownian Motion," The Review of Financial Studies, Society for Financial Studies, vol. 22(2), pages 859-892, February.
    13. Panagiota Daskalopoulos & Paul M. N. Feehan, 2012. "C^{1,1} regularity for degenerate elliptic obstacle problems," Papers 1206.0831, arXiv.org, revised Jan 2016.
    14. repec:oup:restud:v:84:y::i:1:p:182-236. is not listed on IDEAS
    15. repec:zbw:bofrdp:2017_015 is not listed on IDEAS
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    Cited by:

    1. Federico, Salvatore & Ferrari, Giorgio & Schuhmann, Patrick, 2019. "A Model for the Optimal Management of Inflation," Center for Mathematical Economics Working Papers 624, Center for Mathematical Economics, Bielefeld University.
    2. René Carmona, 2022. "The influence of economic research on financial mathematics: Evidence from the last 25 years," Finance and Stochastics, Springer, vol. 26(1), pages 85-101, January.
    3. Jingtang Ma & Zhengyang Lu & Zhenyu Cui, 2022. "Delta family approach for the stochastic control problems of utility maximization," Papers 2202.12745, arXiv.org.
    4. Dylan Possamai & Nizar Touzi, 2020. "Is there a Golden Parachute in Sannikov's principal-agent problem?," Papers 2007.05529, arXiv.org, revised Oct 2022.

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    More about this item

    Keywords

    Principal-agent problem; Regularity properties; Two-dimensional control problem;
    All these keywords.

    JEL classification:

    • G30 - Financial Economics - - Corporate Finance and Governance - - - General

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