Randomisation with moral hazard: A path to existence of optimal contracts
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.
Fields of Study & Subjects
Stochastic processes and financial applications
Mathematical Biology Tumor Growth
Economic theories and models
Publication details
- Journal / source
- The Annals of Applied Probability
- Publisher
- Institute of Mathematical Statistics
- Volume
- 36
- Issue
- 4
- Pages
- 3206–3265
- Publication date
- 1 August 2026
- Language
- EN