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

Summary 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 and unbounded, possibly infinite, horizon, these equations admit a unique solution in appropriately weighted spaces. Our result allows in particular to have a wellposedness result for BSDEs driven by discrete approximations of general martingales.