Admitted symmetries of Backward Stochastic Differential Equations

TL;DR

This paper introduces the concept of admitted Lie groups of transformations for BSDEs and FBSDEs, providing a new symmetry-based framework for analyzing these stochastic equations.

Contribution

It extends the symmetry analysis to backward stochastic differential equations, offering a novel approach following Meleshko et al.'s methodology.

Findings

Defined admitted Lie groups for BSDEs and FBSDEs

Applied the symmetry framework to a specific BSDE example

Provides a foundation for symmetry-based solution methods

Abstract

In this article, we introduce the concept of admitted Lie group of transformations for both backward stochastic differential equations (BSDEs) and forward backward stochastic differential equations (FBSDEs), following the approach of Meleshko et al. An application to BSDE is presented.