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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
Abstract : 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
Keywords : Fully coupled Forward-backward stochastic differential equation Lévy process stochastic differential game
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Journal articles
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https://hal.archives-ouvertes.fr/hal-03359276
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Submitted on : Thursday, September 30, 2021 - 9:37:46 AM
Last modification on : Monday, July 4, 2022 - 3:41:47 PM

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CNRS | UNIV-VALENCIENNES | INSMI | TDS-MACS | LAMAV

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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, De Gruyter, 2014, 22 (3), pp.151-161. ⟨10.1515/rose-2014-0016⟩. ⟨hal-03359276⟩

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