Jean-Paul Décamps, and Stéphane Villeneuve, A two-dimensional control problem arising from dynamic contracting theory, IDEI Working Paper, n. 880, January 2018.


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.


Principal-agent problem; two-dimensional control problem; regularity properties;

JEL codes

  • G30: General

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