The smallest g-supermartingale and reflected BSDE with single and double L 2 obstacles
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 3, pp. 605-630.
@article{AIHPB_2005__41_3_605_0,
     author = {Peng, Shige and Xu, Mingyu},
     title = {The smallest $g$-supermartingale and reflected {BSDE} with single and double ${L}^{2}$ obstacles},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {605--630},
     publisher = {Elsevier},
     volume = {41},
     number = {3},
     year = {2005},
     doi = {10.1016/j.anihpb.2004.12.002},
     zbl = {1071.60049},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2004.12.002/}
}
TY  - JOUR
AU  - Peng, Shige
AU  - Xu, Mingyu
TI  - The smallest $g$-supermartingale and reflected BSDE with single and double ${L}^{2}$ obstacles
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2005
SP  - 605
EP  - 630
VL  - 41
IS  - 3
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpb.2004.12.002/
DO  - 10.1016/j.anihpb.2004.12.002
LA  - en
ID  - AIHPB_2005__41_3_605_0
ER  - 
%0 Journal Article
%A Peng, Shige
%A Xu, Mingyu
%T The smallest $g$-supermartingale and reflected BSDE with single and double ${L}^{2}$ obstacles
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2005
%P 605-630
%V 41
%N 3
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpb.2004.12.002/
%R 10.1016/j.anihpb.2004.12.002
%G en
%F AIHPB_2005__41_3_605_0
Peng, Shige; Xu, Mingyu. The smallest $g$-supermartingale and reflected BSDE with single and double ${L}^{2}$ obstacles. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 3, pp. 605-630. doi : 10.1016/j.anihpb.2004.12.002. http://archive.numdam.org/articles/10.1016/j.anihpb.2004.12.002/

[1] M. Alario-Nazaret, J.P. Lepeltier, B. Marchal, Dynkin games, in: Lecture Notes in Control and Inform. Sci., vol. 43, Springer, Berlin, 1982, pp. 23-42. | MR

[2] A. Bensoussan, A. Friedman, Non-linear variational inequalities and differential games with stopping times, J. Funct. Anal. 16 (1974) 305-352. | MR | Zbl

[3] J.M. Bismut, Sur un probleme de Dynkin, Z. Wahrsch. Verw. Gebiete 39 (1977) 31-53. | MR | Zbl

[4] J. Cvitanic, I. Karatzas, Backward stochastic differential equations with reflection and Dynkin games, Ann. Probab. 24 (4) (1996) 2024-2056. | MR | Zbl

[5] F. Coquet, Y. Hu, J. Memin, S. Peng, Filtration-consistent nonlinear expectations and related g-expectations, Probab. Theory Related Fields 123 (2002) 1-27. | MR | Zbl

[6] C. Dellacherie, P.A. Meyer, Probabilités et Potentiel, I-IV, Hermann, Paris, 1975. | MR | Zbl

[7] C. Dellacherie, P.A. Meyer, Probabilités et Potentiel, V-VIII, Hermann, Paris, 1980. | MR | Zbl

[8] E.B. Dynkin, A.A. Yushkevich, Theorems and Problems in Markov Processes, Plenum Press, New York, 1968.

[9] N. El Karoui, Les aspects probabilistes du contrôle stochastique, in: Ecole d'été de Saint-Flour, 1979, Lecture Notes in Math., vol. 876, Springer, Berlin, 1981, pp. 73-238. | MR | Zbl

[10] N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng, M.C. Quenez, Reflected solutions of backward SDE and related obstacle problems for PDEs, Ann. Probab. 25 (2) (1997) 702-737. | MR | Zbl

[11] N. El Karoui, S.E. Peng, M.C. Quenez, Backward stochastic differential equations in finance, Math. Finance 7 (1997) 1-71. | MR | Zbl

[12] S. Hamadène, Reflected BSDE's with discontinuous barrier and application, Stochastics Stochastics Rep. 74 (3-4) (2002) 571-596. | MR | Zbl

[13] S. Hamadène, J.-P. Lepeltier, Reflected BSDE's and mixed game problem, Stochastics Process. Appl. 85 (2000) 177-188. | MR | Zbl

[14] S. Hamadène, J.-P. Lepeltier, A. Matoussi, Double barrier backward SDEs with continuous coefficient, in: El Karoui N., Mazliak L. (Eds.), Pitman Res. Notes Math. Ser., vol. 364, 1997, pp. 161-171. | MR | Zbl

[15] I. Karatzas, S.E. Shreve, Brownian Motion and Stochastic Calculus, Springer, New York, 1991. | MR | Zbl

[16] J.-P. Lepeltier, M. Xu, Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier, Preprint, 2004. | MR

[17] H. Morimoto, Dynkin games and martingale methods, Stochastics 13 (1984) 213-228. | MR | Zbl

[18] J. Neveu, Discrete-Parameter Martingales, North-Holland, Amsterdam, 1975. | MR | Zbl

[19] E. Pardoux, S. Peng, Adapted solutions of backward stochastic differential equations, Systems Control Lett. 14 (1990) 51-61. | MR | Zbl

[20] S. Peng, Backward SDE and related g-expectation, in: El Karoui N., Mazliak L. (Eds.), Backward Stochastic Differential Equations, Pitman Res. Notes Math. Ser., vol. 364, 1997, pp. 141-159. | MR | Zbl

[21] S. Peng, Monotonic limit theory of BSDE and nonlinear decomposition theorem of Doob-Meyer's type, Probab. Theory Related Fields 113 (1999) 473-499. | MR | Zbl

[22] S. Peng, Nonlinear expectations, nonlinear evaluations and risk measures, in: Lecture Notes in CIME-EMS, Bressanone, Italy, July, 2003, Lecture Notes in Math., Springer, 2004. | MR | Zbl

[23] S. Peng, Dynamical consistent nonlinear evaluations and expectations, Preprint, 2003.

[24] A.V. Shorokhod, Studies in the Theory of the Random Processes, Addison-Wesley, New York, 1965. | MR | Zbl

Cité par Sources :