Fully coupled forward-backward stochastic dynamics and functional differential systems

TL;DR

This paper introduces a novel approach to solving fully coupled forward-backward stochastic dynamics through associated functional differential equations, enabling solutions beyond classical FBSDE frameworks.

Contribution

It presents a unified method that transforms FBSDEs into same-direction equations, avoiding the traditional forward-backward conflict.

Findings

Successfully solves a broad class of FBSDEs outside classical settings.

Develops a new framework using functional differential equations.

Provides solutions where traditional methods struggle.

Abstract

This article introduces and solves a general class of fully coupled forward-backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different types of forward-backward stochastic differential equations (FBSDEs) that do not fit in the classical setting. In our approach, the equations are running in the same time direction rather than in a forward and backward way, and the conflicting nature of the structure of FBSDEs is therefore avoided.