On Generalized Reflected BSDEs with Rcll Obstacle

References

[1] C. Bender and M. Kohlmann, BSDE with stochastic lipschitz condition, J. Appl. Math. Stoch. Anal. 1 (2001), 1–15. Search in Google Scholar

[2] J.-M. Bismut, Conjugate convex functions in optimal stochastic control, J. Math. Anal. Appl. 44 (1973), 384–404. 10.1016/0022-247X(73)90066-8Search in Google Scholar

[3] C. Dellacherie and P.-A. Meyer, Probabilités et potentiel. Chapitres I à IV, Hermann, Paris, 1975. Search in Google Scholar

[4] C. Dellacherie and P.-A. Meyer, Probabilités et potentiel. Chapitres V à VIII, Hermann, Paris, 1980. Search in Google Scholar

[5] N. El Karoui and S.-J. Huang, A general result of existence and uniqueness of backward stochastic differential equations, Backward Stochastic Differential Equations (Paris 1995–1996), Pitman Res. Notes Math. Ser. 364, Longman, Harlow (1997), 27–36. Search in Google Scholar

[6] M. El Otmani, Generalized BSDE driven by a Lévy process, J. Appl. Math. Stoch. Anal. 2006 (2006), Article ID 85407. 10.1155/JAMSA/2006/85407Search in Google Scholar

[7] J. P. Lepeltier and M. Xu, Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier, Statist. Probab. Lett. 75 (2005), 58–66. 10.1016/j.spl.2005.05.016Search in Google Scholar

[8] W. Lü, Reflected BSDE driven by a Lévy process with stochastic Lipschitz coefficient, J. Appl. Math. Inform. 28 (2010), no. 5–6, 1305–1314. Search in Google Scholar

[9] E. Pardoux and S. G. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett. 14 (1990), no. 1, 55–61. 10.1016/0167-6911(90)90082-6Search in Google Scholar

[10] E. Pardoux and S. Zhang, Generalized BSDEs and nonlinear Neumann boundary value problems, Probab. Theory Related Fields 110 (1998), no. 4, 535–558. 10.1007/s004400050158Search in Google Scholar

[11] Y. Ren and M. El Otmani, Generalized reflected BSDEs driven by a Lévy process and an obstacle problem for PDIEs with a nonlinear Neumann boundary condition, J. Comput. Appl. Math. 233 (2010), no. 8, 2027–2043. 10.1016/j.cam.2009.09.037Search in Google Scholar

[12] Y. Ren and N. Xia, Generalized reflected BSDE and an obstacle problem for PDEs with a nonlinear Neumann boundary condition, Stoch. Anal. Appl. 24 (2006), no. 5, 1013–1033. 10.1080/07362990600870454Search in Google Scholar

[13] Z. Xie and N. Xia, Generalized BSDE for Lévy processes under stochastic monotone conditions, Indian J. Pure Appl. Math. 40 (2009), no. 6, 357–371. Search in Google Scholar