Multi-dimensional BSDEs with mean reflection

Qu, Baoyou; Wang, Falei

Abstract

In this paper, we consider multi-dimensional mean reflected backward stochastic differential equations (BSDEs) with possibly non-convex reflection domains along inward normal direction, which were introduced by Briand, Elie and Hu [6] in the scalar case. We first apply a fixed-point argument to establish the uniqueness and existence result under an additional bounded condition on the driver. Then, with the help of a priori estimates, we develop a successive approximation procedure to remove the additional bounded condition for the general case.

Citation

Qu, B., & Wang, F. (2023). Multi-dimensional BSDEs with mean reflection. Electronic Journal of Probability, 28, 1-26. https://doi.org/10.1214/23-ejp991

• Journal Article Type: Article
• Acceptance Date: Jul 4, 2023
• Online Publication Date: Aug 8, 2023
• Publication Date: Aug 8, 2023
• Deposit Date: Feb 14, 2024
• Publicly Available Date: Feb 14, 2024
• Journal: Electronic Journal of Probability
• Electronic ISSN: 1083-6489
• Publisher: Institute of Mathematical Statistics
• Peer Reviewed: Peer Reviewed
• Volume: 28
• Pages: 1-26
• DOI: https://doi.org/10.1214/23-ejp991
• Keywords: Statistics, Probability and Uncertainty; Statistics and Probability
• Public URL: https://durham-repository.worktribe.com/output/2255402