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. doi: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: http://doi.org/10.1080/17442508.2019.1626859

Open Access: Publication channel is not openly available

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


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Other organizations:


Ministry reporting: Yes

Reporting Year: 2020

Preliminary JUFO rating: 1


Last updated on 2020-18-10 at 21:45