Existence and uniqueness results for BSDEs with jumps: the whole nine yards

Antonis Papapantoleon, Dylan Possamaï, Alexandros Saplaouras

Published 2016-07-14Version 1

This paper is devoted to obtaining a wellposedness result for multidimensional BSDEs with possibly unbounded random time horizon and driven by a general martingale in a filtration only assumed to satisfy the usual hypotheses, which in particular may be stochastically discontinuous. We show that for stochastic Lipschitz generators these equations admit a unique solution in appropriately weighted spaces. Unlike the related results in the literature, we do not have to impose any smallness assumption on the size of the jumps of the predictable bracket of the driving martingale or on the Lipschitz constant of the generator.