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A two-dimensional control problem arising from dynamic contracting theory

Author

Listed:
  • Jean-Paul Décamps

    (University of Toulouse Capitole (TSM-R))

  • Stéphane Villeneuve

    (University of Toulouse Capitole (TSM-R))

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," Finance and Stochastics, Springer, vol. 23(1), pages 1-28, January.
    • Handle: RePEc:spr:finsto:v:23:y:2019:i:1:d:10.1007_s00780-018-0376-4
    DOI: 10.1007/s00780-018-0376-4
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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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    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. Jingtang Ma & Zhengyang Lu & Zhenyu Cui, 2022. "Delta family approach for the stochastic control problems of utility maximization," Papers 2202.12745, arXiv.org.
    3. Dylan Possamai & Nizar Touzi, 2020. "Is there a Golden Parachute in Sannikov's principal-agent problem?," Papers 2007.05529, arXiv.org, revised Oct 2022.
    4. 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.

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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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