Electronic Communications in Probability

Existence and Uniqueness of Solutions for BSDEs with Locally Lipschitz Coefficient

Khaled Bahlali

Full-text: Open access

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 $.

Article information

Source
Electron. Commun. Probab., Volume 7 (2002), paper no. 17, 169-179.

Dates
Accepted: 5 August 2002
First available in Project Euclid: 16 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1463434784

Digital Object Identifier
doi:10.1214/ECP.v7-1058

Mathematical Reviews number (MathSciNet)
MR1937902

Zentralblatt MATH identifier
1008.60075

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Backward stochastic differential equations (BSDE) locally Lipschitzfunction

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Bahlali, Khaled. Existence and Uniqueness of Solutions for BSDEs with Locally Lipschitz Coefficient. Electron. Commun. Probab. 7 (2002), paper no. 17, 169--179. doi:10.1214/ECP.v7-1058. https://projecteuclid.org/euclid.ecp/1463434784


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