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Existence and uniqueness of solutions for BSDEs with locally Lipschitz coefficient


 
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1. Title Title of document Existence and uniqueness of solutions for BSDEs with locally Lipschitz coefficient
 
2. Creator Author's name, affiliation, country Khaled Bahlali; CNRS Luminy
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Backward stochastic differential equations (BSDE), locally Lipschitzfunction.
 
3. Subject Subject classification Primary: 60H10.
 
4. Description 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^d\times 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 $.
 
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7. Date (YYYY-MM-DD) 2002-08-05
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1058
 
10. Identifier Digital Object Identifier 10.1214/ECP.v7-1058
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 7
 
12. Language English=en
 
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