# On the solvability of forward-backward stochastic differential equations driven by Teugels Martingales

## TL;DR

This paper proves the existence, uniqueness, stability, and comparison results for fully coupled forward-backward stochastic differential equations driven by Teugels martingales associated with Le9vy processes, extending previous Brownian motion results.

## Contribution

It extends known results on FBSDEs driven by Brownian motion to those driven by general Le9vy processes using Teugels martingales.

## Key findings

- Proved existence and uniqueness of solutions on large time intervals.
- Established stability and comparison theorems for these FBSDEs.
- Extended previous Brownian motion results to Le9vy process-driven equations.

## Abstract

We deal with a class of fully coupled forward-backward stochastic differential equations (FBSDE for short), driven by Teugels martingales associated with some L\'evy process. Under some assumptions on the derivatives of the coefficients, we prove the existence and uniqueness of a global solution on an arbitrarily large time interval. Moreover, we establish stability and comparison theorems for the solutions of such equations. Note that the present work extends known results by Jianfeng Zhang (Discrete Contin. Dyn. Syst. Ser. B 6 (2006), no. 4, 927--940), proved for FBSDEs driven by a Brownian motion, to FBSDEs driven by general L\'evy processes.