On backward stochastic differential equations driven by a family of It\^o's processes

TL;DR

This paper introduces a new class of backward stochastic differential equations driven by a family of Itô processes, establishing foundational results on existence, uniqueness, stability, and comparison.

Contribution

It proposes and analyzes a novel type of BSDE driven by multiple Itô processes, extending the theoretical framework of stochastic differential equations.

Findings

Proved existence and uniqueness of solutions.

Established stability and comparison theorems.

Extended BSDE theory to a new driving process setting.

Abstract

We propose to study a new type of Backward stochastic differential equations driven by a family of It\^o's processes. We prove existence and uniqueness of the solution, and investigate stability and comparison theorem.