Fully coupled forward backward stochastic differential equations driven by Lévy processes and application to differential games

Fouzia Baghery (1) , Nabil Khelfallah (2) , Brahim Mezerdi (2) , Isabelle Massa-Turpin (1)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
2 BISKRA - Université Mohamed Khider de Biskra

We consider a fully coupled forward backward stochastic differential equation driven by a Lévy processes having moments of all orders and an independent Brownian motion. Under some monotonicity assumptions, we prove the existence and uniqueness of solutions on an arbitrarily fixed large time duration. We use this result to prove the existence of an open-loop Nash equilibrium point for non-zero sum stochastic differential games

Mots clés: Fully coupled Forward-backward stochastic differential equation; Lévy process; stochastic differential game

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]; Statistiques [math.ST]

Fouzia Baghery, Nabil Khelfallah, Brahim Mezerdi, Isabelle Massa-Turpin. Fully coupled forward backward stochastic differential equations driven by Lévy processes and application to differential games. Random Operators and Stochastic Equations, 2014, 22 (3), pp.151-161. ⟨10.1515/rose-2014-0016⟩. ⟨hal-03359276⟩