2023/11/22 by Daniel Kršek, Kršek, Daniel, Dylan Possamaï +1
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #General Economics (econ.GN) #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2311.13278
openalex publication_date 2023/11/22 · openalex created_date 2023/11/24 · openalex updated_date 2026/07/28
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.