Journal of Applied Mathematics and Stochastic Analysis, 16:1 (2003), 1-17. Printed in the USA c©2003 by North Atlantic Science Publishing Company BSDE ASSOCIATED WITH LÉVY PROCESSES AND APPLICATION TO PDIE

We deal with backward stochastic differential equations (BSDE for short) driven by Teugel’s martingales and an independent Brownian motion. We study the existence, uniqueness and comparison of solutions for these equations under a Lipschitz as well as a locally Lipschitz conditions on the coefficien...

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Bibliographic Details
Main Authors: K. Bahlali, M. Eddahbi, Universite ́ Cadi Ayyad, Marrakech Maroc, E. Essaky
Other Authors: The Pennsylvania State University CiteSeerX Archives
Format: Text
Language:English
Published: 2002
Subjects:
Lévy Processes
Teugel’s Mar- tingales
Partial Differential Integral Equations
Clark-Ocone Formula
North Atlantic
Online Access:http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.493.1197
http://emis.maths.adelaide.edu.au/journals/HOA/JAMSA/Volume16_1/17.pdf
Description
Summary:We deal with backward stochastic differential equations (BSDE for short) driven by Teugel’s martingales and an independent Brownian motion. We study the existence, uniqueness and comparison of solutions for these equations under a Lipschitz as well as a locally Lipschitz conditions on the coefficient. In the locally Lipschitz case, we prove that if the Lipschitz constant LN behaves as log(N) in the ball B(0, N), then the corresponding BSDE has a unique solution which depends continuously on the on the coefficient and the terminal data. This is done with an unbounded terminal data. As application, we give a probabilistic interpretation for a large class of partial differential integral equations (PDIE for short).

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