# American Institute of Mathematical Sciences

January  2018, 3: 9 doi: 10.1186/s41546-018-0034-y

## Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting

 1. University of Jyvaskyla, Department of Mathematics and Statistics, P. O. Box 35, 40014 Jyvaskyla, Finland; 2. Department of Mathematics and Information Technology, Montanuniversitaet Leoben, Leoben, Austria

Received  January 04, 2018 Revised  November 29, 2018 Published  December 2018

We show that the comparison results for a backward SDE with jumps established in Royer (Stoch. Process. Appl 116:1358-1376, 2006) and Yin and Mao (J. Math. Anal. Appl 346:345-358, 2008) hold under more simplified conditions. Moreover, we prove existence and uniqueness allowing the coefficients in the linear growth- and monotonicity-condition for the generator to be random and time-dependent. In the L2-case with linear growth, this also generalizes the results of Kruse and Popier (Stochastics 88:491-539, 2016). For the proof of the comparison result, we introduce an approximation technique:Given a BSDE driven by Brownian motion and Poisson random measure, we approximate it by BSDEs where the Poisson random measure admits only jumps of size larger than 1/n.
Citation: Christel Geiss, Alexander Steinicke. Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting. Probability, Uncertainty and Quantitative Risk, 2018, 3 (0) : 9-. doi: 10.1186/s41546-018-0034-y
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