In the first part of this paper we give a solution for the one-dimensional reflected backward stochastic differential equation (BSDE for short) when the noise is driven by a Brownian motion and an independent Poisson random measure. The reflecting process is right continuous with left limits (RCLL for short) whose jumps are arbitrary. We first prove existence and uniqueness of the solution for a specific coefficient in using a method based on a combination of penalization and the Snell envelope theory. To show the general result we use a fixed point argument in an appropriate space. The second part of the paper is related to BSDEs with two reflecting barriers. Once more we prove existence and uniqueness of the solution of the BSDE.

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Last updated: 08 Dec 2023