Classical Solutions of Path-dependent PDEs and Functional Forward-Backward Stochastic Systems

TL;DR

This paper establishes a unique correspondence between solutions of a newly introduced path-dependent PDE and functional forward-backward stochastic systems within the framework of functional Itô calculus.

Contribution

It introduces a path-dependent PDE and proves its solution's uniqueness via a functional forward-backward stochastic system, advancing the understanding of stochastic systems and PDEs.

Findings

Unique solution correspondence between path-dependent PDEs and stochastic systems

Framework of functional Itô calculus applied to path-dependent PDEs

Theoretical foundation for future research in stochastic analysis

Abstract

In this paper we study the relationship between functional forward-backward stochastic systems and path-dependent PDEs. In the framework of functional It\^o calculus, we introduce a path-dependent PDE and prove that its solution is uniquely determined by a functional forward-backward stochastic system.