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 .
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, i.e. the filtration may be stochastically discontinuous. We show that for stochastic Lipschitz generators and unbounded, possibly infinite, time horizon, these equations admit a unique solution in appropriately weighted spaces. Our result allows in particular to obtain a wellposedness result for BSDEs driven by discrete-time approximations of general martingales .
R
which in particular
i.e. the filtration
A
and unbounded, possibly infinite, time horizon,
R
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
Our result allows in particular to obtain a wellposedness result for BSDEs driven by discrete-time approximations of general martingales