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In a noise driven by a multivariate point process μ with predictable compensator ν, we prove existence and uniqueness of the reflected backward stochastic differential equation’s solution with a lower obstacle(ξt)t∈[0,T]{(\xi_{t})_{t\in[0,T]}}which is assumed to be a right upper-semicontinuous, but not necessarily right-continuous process, and a Lipschitz driver  f . The result is established by using the Mertens decomposition of optional strong (but not necessarily right continuous) super-martingales, an appropriate generalization of Itô’s formula due to Gal’chouk and Lenglart and some tools from optimal stopping theory. A comparison theorem for this type of equations is given.

Existence and uniqueness for reflected BSDE with multivariate point process and right upper semicontinuous obstacle