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.
Funding Statement
B. Qu acknowledges the financial support from EPSRC grant (No. EP/S005293/2) and the National Natural Science Foundation of China (No. 12171280); F. Wang acknowledges the financial support from the Natural Science Foundation of Shandong Province (No. ZR2021YQ01 and No. ZR2022JQ01), the National Natural Science Foundation of China (No. 12171280 and No. 12031009) and the National Key Research & Development Program of China (No. 2018YFA0703900 and No. 2022YFA1006104).
Acknowledgments
The authors would like to thank the anonymous referees for their valuable suggestions and comments which led to a much improved version of the manuscript.
Citation
Baoyou Qu. Falei Wang. "Multi-dimensional BSDEs with mean reflection." Electron. J. Probab. 28 1 - 26, 2023. https://doi.org/10.1214/23-EJP991
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