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On Generalized Reflected BSDEs with Rcll Obstacle

  • Mohamed El Jamali EMAIL logo und Mohamed El Otmani
Veröffentlicht/Copyright: 8. April 2022
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Abstract

This paper proves the existence and uniqueness theorem for generalized (reflected) backward stochastic differential equations under stochastic Lipschitz and monotone condition. The result is shown by using Picard’s iteration, the Snell envelope theory and the penalization method.

MSC 2010: 60G20; 60H05; 60H15

References

[1] C. Bender and M. Kohlmann, BSDE with stochastic lipschitz condition, J. Appl. Math. Stoch. Anal. 1 (2001), 1–15. Suche 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)90066-8Suche in Google Scholar

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

[4] C. Dellacherie and P.-A. Meyer, Probabilités et potentiel. Chapitres V à VIII, Hermann, Paris, 1980. Suche 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. Suche 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/2006/85407Suche 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.2005.05.016Suche 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. Suche 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)90082-6Suche 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/s004400050158Suche 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.2009.09.037Suche 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. 10.1080/07362990600870454Suche 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. Suche in Google Scholar

Received: 2022-01-08
Revised: 2022-02-25
Accepted: 2022-02-28
Published Online: 2022-04-08
Published in Print: 2022-06-01

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Heruntergeladen am 6.2.2026 von https://www.degruyterbrill.com/document/doi/10.1515/eqc-2022-0001/pdf?lang=de
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