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General time interval multidimensional BSDEs with generators satisfying a weak stochastic-monotonicity condition
December  2021, 6(4): 319-342. doi: 10.3934/puqr.2021016

## Existence, uniqueness and strict comparison theorems for BSDEs driven by RCLL martingales

 1 School of Mathematics, Shandong University, Jinan 250100, Shandong, China 2 School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia 3 Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-661 Warszawa, Poland

E-mail: nietianyang@sdu.edu.cn (Tianyang NIE)

Received  March 25, 2021 Accepted  November 30, 2021 Published  December 2021

Fund Project: The research of M. Rutkowski was supported by the Australian Research Council Discovery Project (Grant No. DP200101550). The work of T. Nie was supported by the National Natural Science Foundation of China (Grant Nos. 12022108, 11971267, 11831010, 61961160732) and Natural Science Foundation of Shandong Province (Grant Nos. ZR2019ZD42, ZR2020ZD24)

The existence, uniqueness, and strict comparison for solutions to a BSDE driven by a multi-dimensional RCLL martingale are developed. The goal is to develop a general multi-asset framework encompassing a wide spectrum of non-linear financial models with jumps, including as particular cases, the setups studied by Peng and Xu [27, 28] and Dumitrescu et al. [7] who dealt with BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump.

Citation: Tianyang Nie, Marek Rutkowski. Existence, uniqueness and strict comparison theorems for BSDEs driven by RCLL martingales. Probability, Uncertainty and Quantitative Risk, 2021, 6 (4) : 319-342. doi: 10.3934/puqr.2021016
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