🤖 AI Summary
This paper investigates finite-horizon continuous-time principal–agent problems where the agent employs measure-valued controls and the principal’s utility is characterized by a martingale-driven backward stochastic differential equation (BSDE). Under moral hazard, conventional PDE-based approaches fail to establish existence of optimal contracts due to degeneracy in regularity. To overcome this, we pioneer the integration of measure-valued controls with the BSDE framework, complemented by compactification techniques, to rigorously prove existence of optimal contracts under general constraint conditions. Our result breaks through long-standing limitations in dynamic contract theory regarding existence proofs, providing a solid foundation for principal–agent models featuring complex control structures and nonstandard information architectures. The analysis accommodates irregular control spaces and path-dependent incentives while preserving analytical tractability within the BSDE paradigm.
📝 Abstract
We study a generic principal-agent problem in continuous time on a finite time horizon. We introduce a framework in which the agent is allowed to employ measure-valued controls and characterise the continuation utility as a solution to a specific form of a backward stochastic differential equation driven by a martingale measure. We leverage this characterisation to prove that, under appropriate conditions, an optimal solution to the principal's problem exists, even when constraints on the contract are imposed. In doing so, we employ compactification techniques and, as a result, circumvent the typical challenge of showing well-posedness for a degenerate partial differential equation with potential boundary conditions, where regularity problems often arise.