A1 Journal article (refereed)
Existence, uniqueness and Malliavin differentiability of Lévy-driven BSDEs with locally Lipschitz driver (2020)
Geiss, C., & Steinicke, A. (2020). Existence, uniqueness and Malliavin differentiability of Lévy-driven BSDEs with locally Lipschitz driver. Stochastics, 92(3), 418-453. https://doi.org/10.1080/17442508.2019.1626859
JYU authors or editors
Publication details
All authors or editors: Geiss, Christel; Steinicke, Alexander
Journal or series: Stochastics
ISSN: 1744-2508
eISSN: 1744-2516
Publication year: 2020
Volume: 92
Issue number: 3
Pages range: 418-453
Publisher: Taylor & Francis
Publication country: United Kingdom
Publication language: English
DOI: https://doi.org/10.1080/17442508.2019.1626859
Publication open access: Not open
Publication channel open access:
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/68631
Publication is parallel published: https://arxiv.org/abs/1805.05851
Abstract
We investigate conditions for solvability and Malliavin differentiability of backward stochastic differential equations driven by a Lévy process. In particular, we are interested in generators which satisfy a local Lipschitz condition in the Z and U variable. This includes settings of linear, quadratic and exponential growths in those variables. Extending an idea of Cheridito and Nam to the jump setting and applying comparison theorems for Lévy-driven BSDEs, we show existence, uniqueness, boundedness and Malliavin differentiability of a solution. The pivotal assumption to obtain these results is a boundedness condition on the terminal value ξ and its Malliavin derivative Dξ. Furthermore, we extend existence and uniqueness theorems to cases where the generator is not even locally Lipschitz in U. BSDEs of the latter type find use in exponential utility maximization.
Keywords: stochastic processes; differential equations; mathematics
Free keywords: BSDEs with jumps; locally Lipschitz generator; quadratic BSDEs; existence and uniqueness of solutions to BSDEs; malliavin differentiability of BSDEs
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2020
JUFO rating: 1
