2017/10/24 by Jean-François Chassagneux, Chassagneux, Jean-François, Adrien Richou +1
Computer Science · Economics, Econometrics and Finance · Engineering · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1710.08989
openalex publication_date 2017/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study existence and uniqueness to multidimensional Reflected Backward Stochastic Differential Equation in an open convex domain, allowing for oblique directions of reflection. In a Markovian framework, combining a priori estimates for penalised equations and compactness arguments, we obtain existence results under quite weak assumptions on the driver of the BSDEs and the direction of reflection, which is allowed to depend on both Y and Z. In a non Markovian framework, we obtain existence and uniqueness result for direction of reflection depending on time and Y. We make use in this case of stability estimates that require some smoothness condition on the domain and the direction of reflection. In a last Section, we illustrate the application of our theoretical results by introducing randomised switching problems.