Research Article | Open Access
Jiajie Wang, Qikang Ran, Qihong Chen, " Solutions of BSDEs with Stochastic Lipschitz Condition", International Journal of Stochastic Analysis, vol. 2007, Article ID 078196, 14 pages, 2007. https://doi.org/10.1155/2007/78196
Solutions of BSDEs with Stochastic Lipschitz Condition
We are concerned with the solutions of a special class of backward stochastic differential equations which are driven by a Brownian motion, where the uniform Lipschitz continuity is replaced by a stochastic one. We prove the existence and uniqueness of the solution in with .
- É. Pardoux and S. G. Peng, “Adapted solution of a backward stochastic differential equation,” Systems & Control Letters, vol. 14, no. 1, pp. 55–61, 1990.
- N. El Karoui, S. G. Peng, and M. C. Quenez, “Backward stochastic differential equations in finance,” Mathematical Finance, vol. 7, no. 1, pp. 1–71, 1997.
- Ph. Briand and R. Carmona, “BSDEs with polynomial growth generators,” Journal of Applied Mathematics and Stochastic Analysis, vol. 13, no. 3, pp. 207–238, 2000.
- Ph. Briand, B. Delyon, Y. Hu, E. Pardoux, and L. Stoica, “ solutions of backward stochastic differential equations,” Stochastic Processes and Their Applications, vol. 108, no. 1, pp. 109–129, 2003.
- N. El Karoui and S.-J. Huang, “A general result of existence and uniqueness of backward stochastic differential equations,” in Backward Stochastic Differential Equations (Paris, 1995-1996), vol. 364 of Pitman Research Notes in Mathematics Series, pp. 27–36, Longman, Harlow, London, UK, 1997.
- C. Bender and M. Kohlmann, “BSDEs with stochastic Lipschitz condition,” http://cofe.uni-konstanz.de/Papers/dp00_08.pdf preprint..
Copyright © 2007 Jiajie Wang et al. 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.