A general comparison theorem for 1-dimensional anticipated BSDEs

TL;DR

This paper establishes a general comparison theorem for 1-dimensional anticipated backward stochastic differential equations (ABSDEs) with generators depending on the anticipated Z-term, advancing the theoretical understanding of ABSDEs.

Contribution

It introduces a broad comparison theorem for 1D ABSDEs with generators involving the anticipated Z-term, expanding existing theoretical frameworks.

Findings

Proves a general comparison theorem for 1D ABSDEs

Handles generators depending on the anticipated Z-term

Enhances theoretical understanding of ABSDEs

Abstract

Anticipated backward stochastic differential equation (ABSDE) studied the first time in 2007 is a new type of stochastic differential equations. In this paper, we establish a general comparison theorem for 1-dimensional ABSDEs with the generators depending on the anticipated term of $Z$.