Forward-backward SDEs with distributional coefficients
Abstract
Forward-backward stochastic differential equations (FBSDEs) have attracted significant attention since they were introduced almost 30 years ago, due to their wide range of applications, from solving non-linear PDEs to pricing American-type options. Here, we consider two new classes of multidimensional FBSDEs with distributional coefficients (elements of a Sobolev space with negative order). We introduce a suitable notion of a solution, show existence and uniqueness of a strong solution of the first FBSDE, and weak existence for the second. We establish a link with PDE theory via a nonlinear Feynman-Kac representation formula. The associated semi-linear second order parabolic PDE is the same for both FBSDEs, also involves distributional coefficients and has not previously been investigated; our analysis uses mild solutions, Sobolev spaces and semigroup theory.
Keywords
Cite
@article{arxiv.1605.01558,
title = {Forward-backward SDEs with distributional coefficients},
author = {Elena Issoglio and Shuai Jing},
journal= {arXiv preprint arXiv:1605.01558},
year = {2022}
}
Comments
40 pages, no figures - new improved version with shorter proof of Thm 18, extended results in Thm 25 and Thm 27. Other minor clarifications added