BSDE driven by Poisson point processes with discontinuous coefficient

In this paper, we deal with the one-dimensional backward stochastic differential equation (BSDE) driven by Poisson processes. By means of the comparison theorem, we first prove the existence of a (minimal) solution for BSDE where the coefficient is continuous and satisfies an improved linear growth assumption. Then we extend the result to the case where the coefficient is left or right continuous.