$L^p$-Solutions and Comparison Results for L\'evy Driven BSDEs in a Monotonic, General Growth Setting

Stefan Kremsner; Alexander Steinicke

$L^p$-Solutions and Comparison Results for L\'evy Driven BSDEs in a Monotonic, General Growth Setting

Probability 2020-11-03 v4

Authors: Stefan Kremsner , Alexander Steinicke

Abstract

We present a unified approach to $L^p$ -solutions ( $p > 1$ ) of multidimensional backward stochastic differential equations (BSDEs) driven by L\'evy processes and more general filtrations. New existence, uniqueness and comparison results are obtained. The generator functions obey a time-dependent extended monotonicity (Osgood) condition in the $y$ -variable and have general growth in $y$ . Within this setting, the results generalize those of Royer (2006), Yin and Mao (2008), Yao (2017), Kruse and Popier (2016/2017) and Geiss and Steinicke (2018).

Keywords

backward stochastic differential equations levy processes l^p-solutions comparison theorem osgood condition general growth existence and uniqueness

Cite

@article{arxiv.1909.06181,
  title  = {$L^p$-Solutions and Comparison Results for L\'evy Driven BSDEs in a Monotonic, General Growth Setting},
  author = {Stefan Kremsner and Alexander Steinicke},
  journal= {arXiv preprint arXiv:1909.06181},
  year   = {2020}
}

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