Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 85407, 25 pages
Generalized BSDE driven by a Lévy process
Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh BP 2390, Morocco
Received 4 March 2005; Accepted 14 June 2006
Copyright © 2006 Mohamed El Otmani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study the solution of one-dimensional generalized backward stochastic differential
equation driven by Teugels martingales and an independent Brownian motion. We prove existence and uniqueness of the solution when the coefficient verifies some conditions of Lipschitz. If the coefficient is left continuous, increasing,
and bounded, we prove the existence of a solution.