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Existence and uniqueness for $\mathbb{D}$-solutions of reflected BSDEs with two barriers without Mokobodzki's condition
1. | Université de Sfax, Faculté des Sciences de Sfax, département de mathématiques, BP 1171 Sfax 3000, Tunisia |
References:
[1] |
Ph. Briand, B. Delyon, Y. Hu, E. Pardoux and L. Stoica, $L^p$ solutions of backward stochastic differential equations, Stochastic Process. Appl., 108 (2003), 109-129.
doi: 10.1016/S0304-4149(03)00089-9. |
[2] |
J. Cvitanic and I. Karatzas, Backward stochastic differential equations with reflection and Dynkin games, Annals of probability, 24 (1996), 2024-2056.
doi: 10.1214/aop/1041903216. |
[3] |
C. Dellacherie and P. A. Meyer, Probabilit et Potentiel I-IV, Hermann, Paris, 1975. |
[4] |
C. Dellacherie and P. A. Meyer, Probabilit et Potentiel V-VIII Hermann, Paris, 1980 |
[5] |
B. El Asri, S. Hamade and H. Wang, $L^p$ solutions for doubly reflected backward stochastic differential equations, Stochastic Analysis and Applications, 29 (2011), 907-932.
doi: 10.1080/07362994.2011.564442. |
[6] |
N. El Karoui, Les aspects probabilistes du contrôle stochastique, in Ecole dEtde Probabilit de Saint-Flour IX, Volume 876 of the series Lecture Notes in Mathematics , (1979), 73-238. |
[7] |
N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng and M. C. Quenez, Reflected solutions of backward SDE's, and related obstacle problems for PDEs, Ann Probab., 25 (1997), 702-737.
doi: 10.1214/aop/1024404416. |
[8] |
S. Hamadène, Mixed zero-sum differential game and American game options, SIAM J. Control Optim., 45 (2006), 496-518.
doi: 10.1137/S036301290444280X. |
[9] |
S. Hamadène, Reflected BSDE's with discontinuous barriers and application, Stochastics and Sotochastics Reports, (2002), 571-596. |
[10] |
S. Hamadène and M. Hassani, BSDEs with two reflecting barriers: the general result, Probability theory and related fields, 132 (2005), 237-264.
doi: 10.1007/s00440-004-0395-2. |
[11] |
S. Hamadène and M. Jeanblanc, On the stopping and starting problem: application to reversible investment, Mathematics of Operations Research, 32 (2007), 182-192.
doi: 10.1287/moor.1060.0228. |
[12] |
S. Hamadène and J. P. Lepeltier, Reflected backward SDE's and mixed game problems, Stochastic Processes and their Applications, 85 (2000), 177-188.
doi: 10.1016/S0304-4149(99)00072-1. |
[13] |
S. Hamadène and Y. Ouknine, Reflected backward stochastic differential equation with jumps and random obstacle, Electronic Journal of Probability. 8 (2003), 1-20.
doi: 10.1214/EJP.v8-124. |
[14] |
S. Hamadène and A. Popier, $L^p$ solutions for reflected backward stochastic differential equations, Stochastics and Dynamics, 12 (2012), 35 pages.
doi: 10.1142/S0219493712003651. |
[15] |
T. Klimsiak, Reflected BSDEs with monotone generator, Electronic Journal of Probability, 107 (2012), 1-25.
doi: 10.1214/EJP.v17-1759. |
[16] |
T. Klimsiak, BSDEs with monotone generator and two irregular reflecting barriers, Bulletin des Sciences Math閙atiques, 137 (2013), 268-321.
doi: 10.1016/j.bulsci.2012.06.006. |
[17] |
E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equations, Systems and Control Letters, 14, (1990), 55-61.
doi: 10.1016/0167-6911(90)90082-6. |
[18] |
S. Peng, Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type, Probability Theory and Related Fields, 113 (1999), 473-499.
doi: 10.1007/s004400050214. |
[19] |
E. P. Protter, Stochastic Integration and Differential Equations, 2nd edition, Springer, New York, 2000. |
[20] |
D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, Springer, New York, 1994. |
[21] |
A. Roskoz and L. Slominski, $L^p$ solutions for reflected BSDEs under monotonicity condition, Stochastic Processes and their Applications, 122 (2012), 3875-3900.
doi: 10.1016/j.spa.2012.07.006. |
show all references
References:
[1] |
Ph. Briand, B. Delyon, Y. Hu, E. Pardoux and L. Stoica, $L^p$ solutions of backward stochastic differential equations, Stochastic Process. Appl., 108 (2003), 109-129.
doi: 10.1016/S0304-4149(03)00089-9. |
[2] |
J. Cvitanic and I. Karatzas, Backward stochastic differential equations with reflection and Dynkin games, Annals of probability, 24 (1996), 2024-2056.
doi: 10.1214/aop/1041903216. |
[3] |
C. Dellacherie and P. A. Meyer, Probabilit et Potentiel I-IV, Hermann, Paris, 1975. |
[4] |
C. Dellacherie and P. A. Meyer, Probabilit et Potentiel V-VIII Hermann, Paris, 1980 |
[5] |
B. El Asri, S. Hamade and H. Wang, $L^p$ solutions for doubly reflected backward stochastic differential equations, Stochastic Analysis and Applications, 29 (2011), 907-932.
doi: 10.1080/07362994.2011.564442. |
[6] |
N. El Karoui, Les aspects probabilistes du contrôle stochastique, in Ecole dEtde Probabilit de Saint-Flour IX, Volume 876 of the series Lecture Notes in Mathematics , (1979), 73-238. |
[7] |
N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng and M. C. Quenez, Reflected solutions of backward SDE's, and related obstacle problems for PDEs, Ann Probab., 25 (1997), 702-737.
doi: 10.1214/aop/1024404416. |
[8] |
S. Hamadène, Mixed zero-sum differential game and American game options, SIAM J. Control Optim., 45 (2006), 496-518.
doi: 10.1137/S036301290444280X. |
[9] |
S. Hamadène, Reflected BSDE's with discontinuous barriers and application, Stochastics and Sotochastics Reports, (2002), 571-596. |
[10] |
S. Hamadène and M. Hassani, BSDEs with two reflecting barriers: the general result, Probability theory and related fields, 132 (2005), 237-264.
doi: 10.1007/s00440-004-0395-2. |
[11] |
S. Hamadène and M. Jeanblanc, On the stopping and starting problem: application to reversible investment, Mathematics of Operations Research, 32 (2007), 182-192.
doi: 10.1287/moor.1060.0228. |
[12] |
S. Hamadène and J. P. Lepeltier, Reflected backward SDE's and mixed game problems, Stochastic Processes and their Applications, 85 (2000), 177-188.
doi: 10.1016/S0304-4149(99)00072-1. |
[13] |
S. Hamadène and Y. Ouknine, Reflected backward stochastic differential equation with jumps and random obstacle, Electronic Journal of Probability. 8 (2003), 1-20.
doi: 10.1214/EJP.v8-124. |
[14] |
S. Hamadène and A. Popier, $L^p$ solutions for reflected backward stochastic differential equations, Stochastics and Dynamics, 12 (2012), 35 pages.
doi: 10.1142/S0219493712003651. |
[15] |
T. Klimsiak, Reflected BSDEs with monotone generator, Electronic Journal of Probability, 107 (2012), 1-25.
doi: 10.1214/EJP.v17-1759. |
[16] |
T. Klimsiak, BSDEs with monotone generator and two irregular reflecting barriers, Bulletin des Sciences Math閙atiques, 137 (2013), 268-321.
doi: 10.1016/j.bulsci.2012.06.006. |
[17] |
E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equations, Systems and Control Letters, 14, (1990), 55-61.
doi: 10.1016/0167-6911(90)90082-6. |
[18] |
S. Peng, Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type, Probability Theory and Related Fields, 113 (1999), 473-499.
doi: 10.1007/s004400050214. |
[19] |
E. P. Protter, Stochastic Integration and Differential Equations, 2nd edition, Springer, New York, 2000. |
[20] |
D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, Springer, New York, 1994. |
[21] |
A. Roskoz and L. Slominski, $L^p$ solutions for reflected BSDEs under monotonicity condition, Stochastic Processes and their Applications, 122 (2012), 3875-3900.
doi: 10.1016/j.spa.2012.07.006. |
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