Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting
Geiss, C., & Steinicke, A. (2018). Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting. Probability, Uncertainty and Quantitative Risk, 3 (9), 1-33. doi:10.1186/s41546-018-0034-y
Published inProbability, Uncertainty and Quantitative Risk
© The Author(s), 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.