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On the well‐posedness of coupled forward–backward stochastic differential equations driven by Teugels martingales
Author(s) -
Guerdouh Dalila,
Khelfallah Nabil,
Mezerdi Brahim
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6696
Subject(s) - mathematics , stochastic differential equation , martingale (probability theory) , uniqueness , brownian motion , jump , comparison theorem , lévy process , mathematical analysis , statistics , physics , quantum mechanics
We deal with a class of fully coupled forward–backward stochastic differential equations (FBSDEs), driven by Teugels martingales associated with a general Lévy 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 proved for FBSDEs driven by a Brownian motion, by using martingale techniques related to jump processes, to overcome the lack of continuity.