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

Abstract

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.

arXiv comment48 pages, final version, forthcoming in the Electronic Journal of Probability

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• Stability results for martingale representations: the general case
• On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples
• Reflected BSDEs and doubly reflected BSDEs driven by RCLL martingales
• Existence, uniqueness and strict comparison theorems for backward stochastic differential equations driven by RCLL martingales
• Reflections on BSDEs
• A Framework of BSDEs with Stochastic Lipschtz Coefficients through Time Change