Multi-dimensional BSDEs whose terminal values are bounded and have bounded Malliavin derivatives
Probability
2018-08-31 v3
Abstract
We consider a class of multi-dimensional BSDEs on a finite time horizon (containing in particular Lipschitzian-quadratic BSDEs), whose terminal values are bounded as well as their corresponding Malliavin derivatives. We prove two results. The first one is an exponential integrability condition which determines when a BSDE in this class has a solution up to a given time horizon. In the second result, via an ordinary differential equation, we compute a minimum horizon up to which any BSDE of this class has a solution. The combination of these two results leads to a new scheme to solve quadratic BSDEs.
Cite
@article{arxiv.1711.02944,
title = {Multi-dimensional BSDEs whose terminal values are bounded and have bounded Malliavin derivatives},
author = {Shiqi Song},
journal= {arXiv preprint arXiv:1711.02944},
year = {2018}
}
Comments
In this third arXiv version, the Introduction has been rewritten and new applications have been added to better illustrate the main results