On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples
We extend the monotone stability approach for backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure, which can be of infinite activity and time-inhomogeneous with non-deterministic compensator. The BSDE generator function can be non-convex and needs not to satisfy classical global Lipschitz conditions in the jump integrand. We contribute concrete criteria, that are easy to verify, and extended results for comparison and for existence and uniqueness of bounded solutions to BSDEs with jumps. The scope of results, applicability of assumptions and differences to related results by some alternative approaches are demonstrated by several examples for control problems from finance.
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