A Continuous-Time Dynamic Contracting Problem with Limited Liability and Finite Horizon

Stéphane Villeneuve, Andrea Bovo and Tiziano De Angelis

No 26-1772, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: We perform a detailed study of a principal–agent problem in a continuous time version of the celebrated Holmstr¨om–Milgrom model (Econometrica 55 (2), 1987) where we add limited liability for the Agent. We develop a probabilistic methodology to prove that the Principal’s value function is the unique classical solution to a fully nonlinear and fully degenerate partial differential equation (PDE) with Cauchy-Dirichlet boundary conditions on [0, T ]×[0, ∞). Indeed, we also prove infinite continuous differentiability of the solution in the interior of the domain. The strength of our regularity result is such that we can ensure existence of optimal controls in strong form—a rare occurrence in dynamic contracting—and we obtain fine properties of the optimal control map, including a characterisation via a further nonlinear degenerate PDE.

Keywords: fully nonlinear and fully degenerate HJB équations; finite horizon; time-changed diffusions; dynamic contracting; limited liability (search for similar items in EconPapers)
Date: 2026-09-16
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.tse-fr.eu/sites/default/files/TSE/docu ... 2026/wp_tse_1772.pdf Full Text (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tse:wpaper:132158

Access Statistics for this paper

More papers in TSE Working Papers from Toulouse School of Economics (TSE) Contact information at EDIRC.
Bibliographic data for series maintained by ().