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 editorsGeiss, Christel; Steinicke, Alexander

Journal or seriesStochastics



Publication year2020


Issue number3

Pages range418-453

PublisherTaylor & Francis

Publication countryUnited Kingdom

Publication languageEnglish


Publication open accessNot open

Publication channel open access

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/68631

Publication is parallel publishedhttps://arxiv.org/abs/1805.05851


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.

Keywordsstochastic processesdifferential equationsmathematics

Free keywordsBSDEs with jumps; locally Lipschitz generator; quadratic BSDEs; existence and uniqueness of solutions to BSDEs; malliavin differentiability of BSDEs

Contributing organizations

Other organizations:

Ministry reportingYes

Reporting Year2020

JUFO rating1

Last updated on 2024-03-04 at 21:07