On the solvability of forward-backward stochastic differential equations driven by Teugels Martingales
Probability
2017-01-31 v1 Optimization and Control
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.
Keywords
Cite
@article{arxiv.1701.08396,
title = {On the solvability of forward-backward stochastic differential equations driven by Teugels Martingales},
author = {Dalila Guerdouh and Nabil Khelfallah and Brahim Mezerdi},
journal= {arXiv preprint arXiv:1701.08396},
year = {2017}
}
Comments
23 pages, submitted for publication in Stochastic Analysis and Applications