General Fully Coupled Forward Backward Stochastic Differential Equations with delayed generator

TL;DR

This paper investigates various types of backward stochastic differential equations with delayed generators, establishing existence and uniqueness results under specific conditions, and extends these findings to fully coupled forward-backward systems with delays.

Contribution

It introduces new existence and uniqueness theorems for BSDEs with delayed generators and extends these results to fully coupled forward-backward stochastic systems with delays.

Findings

Proved existence and uniqueness for non-homogeneous BSDEs with delays.

Extended results to fully coupled forward-backward systems with delayed coefficients.

Established conditions under which solutions are well-defined and unique.

Abstract

This paper is devoted to study different type of BSDE with delayed generator. We first establish an existence and uniqueness result under delayed Lipschitz condition for non homogenous backward stochastic differential equation with delayed generator. Next, existence and uniqueness result for general fully coupled forward backward stochastic differential equation with delayed coefficients has been derived.