2018/12/17 by Brahim Baadi, Youssef Ouknine
Mathematics · #math.PR #msc:60K35 #msc:82B43
published as ALEA, Lat. Am. J. Probab. Math. Stat. 14, 201-218 (2017) · Received by the editors May 6th, 2016; accepted March 3rd, 2017. arXiv admin note: text overlap with arXiv:1504.06094
arxiv created 2018/12/17 · arxiv updated 2018/12/20
We prove existence and uniqueness of the reflected backward stochastic differential equation's (RBSDE) solution with a lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous in a filtration that supports a Brownian motion W and an independent Poisson random measure π. The result is established by using some tools from the general theory of processes such as Mertens decomposition of optional strong (but not necessarily right continuous) supermartingales and some tools from optimal stopping theory, as well as an appropriate generalization of Itô's formula due to Gal'chouk and Lenglart. Two applications on dynamic risk measure and on optimal stopping will be given.