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. https://doi.org/10.1186/s41546-018-0034-y
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Probability, Uncertainty and Quantitative RiskDate
2018Copyright
© 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.
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Shandong DaxueISSN Search the Publication Forum
2367-0126Keywords
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