Finance and Stochastics

, Volume 23, Issue 1, pp 1–28 | Cite as

A two-dimensional control problem arising from dynamic contracting theory

  • Jean-Paul Décamps
  • Stéphane VilleneuveEmail author


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.


Principal–agent problem Two-dimensional control problem Regularity properties 

Mathematics Subject Classification (2010)

49L20 60G40 91G50 

JEL Classification



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Toulouse School of EconomicsUniversity of Toulouse Capitole (TSM-R)ToulouseFrance

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