A two-dimensional control problem arising from dynamic contracting theory

Jean-Paul Décamps (1) , Stéphane Villeneuve (1)

1 TSE-R - Toulouse School of Economics

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

Mots clés: Principal-agent problem; Regularity properties; Two-dimensional control problem

Domaines: Gestion et management

Jean-Paul Décamps, Stéphane Villeneuve. A two-dimensional control problem arising from dynamic contracting theory. Finance and Stochastics, 2019, 23 (1), pp.1-28. ⟨10.1007/s00780-018-0376-4⟩. ⟨halshs-02282092⟩