In this work, we deal with a backward stochastic differential equation with respect to a Brownian motion and a Poisson random measure. We first establish existence and uniqueness of solution in the case of non-Lipschitz drift. In the second part, we prove a Large Deviation Principle for a family of solutions.
"BSDE with jumps and non-Lipschitz coefficients: Application to large deviations." Braz. J. Probab. Stat. 28 (1) 96 - 108, February 2014. https://doi.org/10.1214/12-BJPS197