Non-Markovian Fully Coupled Forward-Backward Stochastic Systems and Classical Solutions of Path-dependent PDEs

TL;DR

This paper establishes a connection between non-Markovian stochastic systems and path-dependent PDEs, proving that under certain conditions, the stochastic system uniquely solves the PDE using functional Itô calculus.

Contribution

It introduces a framework linking non-Markovian forward-backward stochastic systems with classical solutions of path-dependent PDEs, expanding the theoretical understanding.

Findings

Proves the existence and uniqueness of classical solutions to path-dependent PDEs.

Establishes that the stochastic system provides the unique solution under mild hypotheses.

Utilizes functional Itô calculus to define and analyze solutions.

Abstract

This paper explores the relationship between non-Markovian fully coupled forward-backward stochastic systems and path-dependent PDEs. The definition of classical solution for the path-dependent PDE is given within the framework of functional It\^{o} calculus. Under mild hypotheses, we prove that the forward-backward stochastic system provides the unique classical solution to the path-dependent PDE.