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Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting
Christel Geiss1, Alexander Steinicke2
11University of Jyvaskyla, Department of Mathematics and Statistics, P.O. Box 35, Jyvaskyla, 40014 Finland.
Abstract:
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 L 2-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.
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