Reflected backward stochastic differential equation with jumps and random obstacle (Q1858672)

Reflected backward stochastic differential equations (BSDE in short) were introduced by \textit{N. El Karoui}, \textit{C. Kapoudjian}, \textit{E. Pardoux}, \textit{S. Peng} and \textit{M. C. Quenez} [Ann. Probab. 25, No. 2, 702-737 (1997; Zbl 0899.60047)]. The authors of the present paper study a one-dimensional reflected BSDE whose noise is driven by a Brownian motion and an independent Poisson random measure. By two methods -- by penalization and by the Snell envelope theory -- plus some fix point arguments, they show that existence and uniqueness of a solution hold. Further they make the link between these reflected BSDEs and integro-differential mixed stochastic optimal control.