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A two-dimensional control problem arising from dynamic contracting theory

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  • Décamps, Jean-Paul
  • Villeneuve, Stéphane

Abstract

We study a corporate finance dynamic contracting model in which the firm's growth rate fluctuates and is impacted by the unobservable effort exercised by the manager. We show that the principal's problem takes the form of a two-dimensional Markovian control problem. We prove regularity properties of the value function that are instrumental in the construction of the optimal contract that implements full effort, which we derive explicitly. These regularity results appear in some recent economic studies but with heuristic proofs that do not clarify the importance of the regularity of the value function at the boundaries.

Suggested Citation

  • Décamps, Jean-Paul & Villeneuve, Stéphane, 2018. "A two-dimensional control problem arising from dynamic contracting theory," IDEI Working Papers 880, Institut d'Économie Industrielle (IDEI), Toulouse.
    • Handle: RePEc:ide:wpaper:32396
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    References listed on IDEAS

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    1. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
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    6. Peter M. Demarzo & Yuliy Sannikov, 2017. "Learning, Termination, and Payout Policy in Dynamic Incentive Contracts," Review of Economic Studies, Oxford University Press, vol. 84(1), pages 182-236.
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    8. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
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    12. Zhiguo He, 2009. "Optimal Executive Compensation when Firm Size Follows Geometric Brownian Motion," 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
    16. repec:zbw:bofrdp:2017_014 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; two-dimensional control problem; regularity properties;
    All these keywords.

    JEL classification:

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

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