2016/07/31 by Dirk Becherer, Martin Büttner, Klebert Kentia · 1 citation
Mathematics · Economics, Econometrics and Finance · #math.PR #math.OC #q-fin.MF #msc:60G57 #msc:60H20 #msc:93E20 #msc:60G51 #msc:91G80
paper · pdf · doi:10.1007/978-3-030-22285-7_1
28 pages. Added DOI https://link.springer.com/chapter/10.1007%2F978-3-030-22285-7_1 for final publication, corrected typo (missing gamma) in example 4.15
arxiv created 2019/11/20 · arxiv updated 2019/11/21
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 for 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 to satisfy global Lipschitz conditions in the jump integrand. We contribute concrete 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∞-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.