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Existence and Uniqueness of Solutions for Multi-dimensional Reflected Backward Stochastic Differential Equations with Diagonally Quadratic Generators

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Abstract

In this paper, we study multi-dimensional reflected backward stochastic differential equations (BSDEs) with diagonally quadratic generators. Using the comparison theorem for diagonally quadratic BSDEs established recently in Luo (Disc Contin Dyn Syst 41(6):2543–2557, 2021), we obtain the existence and uniqueness of a solution by a penalization method. Moreover, we provide a comparison theorem.

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Acknowledgements

The authors would like to thank the associate editor and referee for their constructive comments and suggestions, which have significantly improved the manuscript. This work is supported by the National Natural Science Foundation of China (Grant No. 12101400).

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  1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China

    Yuyang Chen & Peng Luo

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  1. Yuyang Chen
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  2. Peng Luo
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Correspondence to Peng Luo.

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Chen, Y., Luo, P. Existence and Uniqueness of Solutions for Multi-dimensional Reflected Backward Stochastic Differential Equations with Diagonally Quadratic Generators. J Theor Probab 36, 1698–1719 (2023). https://doi.org/10.1007/s10959-022-01224-7

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