Mild Solutions for Path-Dependent Parabolic PDEs with Neumann Boundary Conditions via Generalized BSDEs
Probability
2026-01-23 v1
Abstract
We study a system of Forward-Backward Stochastic Differential Equations (FBSDEs) with time-delayed generators. The forward process includes a reflection component expressed via a Stieltjes integral, while the backward process takes the form of a Generalized BSDE. We establish the connection between this FBSDE system and non-linear path-dependent PDEs with Neumann boundary conditions by deriving a representation formula.
Keywords
Cite
@article{arxiv.2601.16178,
title = {Mild Solutions for Path-Dependent Parabolic PDEs with Neumann Boundary Conditions via Generalized BSDEs},
author = {Luca Di Persio and Matteo Garbelli and Adrian Zalinescu},
journal= {arXiv preprint arXiv:2601.16178},
year = {2026}
}