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2019 | OriginalPaper | Chapter

On the Monotone Stability Approach to BSDEs with Jumps: Extensions, Concrete Criteria and Examples

Authors : Dirk Becherer, Martin Büttner, Klebert Kentia

Published in: Frontiers in Stochastic Analysis–BSDEs, SPDEs and their Applications

Publisher: Springer International Publishing

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Abstract

We show a concise extension of the monotone stability approach to backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure of jumps, which could be of infinite activity with a non-deterministic and time-inhomogeneous compensator. The BSDE generator function can be non-convex and needs not satisfy global Lipschitz conditions in the jump integrand. We contribute concrete sufficient criteria, that are easy to verify, for results on existence and uniqueness of bounded solutions to BSDEs with jumps, and on comparison and a-priori \(L^\infty \)-bounds. Several examples and counter examples are discussed to shed light on the scope and applicability of different assumptions, and we provide an overview of major applications in finance and optimal control.

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next chapter On the Wellposedness of Some McKean Models with Moderated or Singular Diffusion Coefficient
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Metadata
Title
On the Monotone Stability Approach to BSDEs with Jumps: Extensions, Concrete Criteria and Examples
Authors
Dirk Becherer
Martin Büttner
Klebert Kentia
Copyright Year
2019
Book
Frontiers in Stochastic Analysis–BSDEs, SPDEs and their Applications

Print ISBN: 978-3-030-22284-0

Electronic ISBN: 978-3-030-22285-7

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-22285-7_1