Existence and uniqueness of solutions for BSDEs with locally Lipschitz coefficient
Khaled Bahlali, CNRS Luminy
Abstract
We deal with multidimensional backward stochastic differential
equations (BSDE) with locally Lipschitz coefficient in both variables $ y,z
$ and an only square integrable terminal data. Let $ L_N $ be the Lipschitz
constant of the coefficient on the ball $ B(0,N) $ of $ R^dtimes R^{dr} $.
We prove that if $ L_N = O (sqrt {log N }) $, then the corresponding BSDE
has a unique solution. Moreover, the stability of the solution is established
under the same assumptions. In the case where the terminal data
is bounded, we establish the existence and uniqueness of the solution also
when the coefficient has an arbitrary growth (in $ y $) and without restriction
on the behaviour of the Lipschitz constant $ L_N $.
Full text: PDF | PostScript
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona.
The preferred way is to send a scanned (jpeg or pdf) copy of the signed copyright form to the managing editor Philippe Carmona at ejpecpme@math.univ-nantes.fr.
If a paper has several authors, the corresponding author signs the copyright form
on behalf of all the authors.