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Controlled reflected mean-field backward stochastic differential equations coupled with value function and related PDEs
1. | School of Mathematics and Statistics, Shandong University, Weihai, Weihai, 264209, China, China |
References:
[1] |
G. Barles, R. Buckdahn and E. Pardoux, Backward stochastic differential equations and integral-partial differential equations, Stoch. Stoch. Rep., 60 (1997), 57-83.
doi: 10.1080/17442509708834099. |
[2] |
R. Buckdahn and J. Li, Stochastic differential games and viscosity solutions of Hamilton- Jacobi-Bellman-Isaacs equations, SIAM. J. Control. Optim., 47 (2008), 444-475.
doi: 10.1137/060671954. |
[3] |
R. Buckdahn and J. Li, Stochastic differential games with reflection and related obstacle problems for Isaacs equations, Acta Math. Appl. Sin.-Enql. Ser., 27 (2011), 647-678.
doi: 10.1007/s10255-011-0068-8. |
[4] |
R. Buckdahn, B. Djehiche, J. Li and S. Peng, Mean-field backward stochastic differential equations. A limit approach, Ann. Probab., 37 (2009), 1524-1565.
doi: 10.1214/08-AOP442. |
[5] |
R. Buckdahn, J. Li and S. Peng, Mean-field backward stochastic differential equations and related partial differential equations, Stoch. Proc. App., 119 (2009), 3133-3154.
doi: 10.1016/j.spa.2009.05.002. |
[6] |
M. G. Crandall, H. Ishii and P. L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27 (1992), 1-67.
doi: 10.1090/S0273-0979-1992-00266-5. |
[7] |
T. Hao and J. Li, Backward stochastic differential equations coupled with value function and related optimal control problems, Abstract Appl. Anal., 2014 (2014), Art. ID 262713, 17 pp.
doi: 10.1155/2014/262713. |
[8] |
N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng and M. C. Quenez, Reflected solutions of backward SDE's, and related obstacle problems for PDE's, Ann. Probab., 25 (1997), 702-737.
doi: 10.1214/aop/1024404416. |
[9] |
J. Li, Reflected mean-field backward stochastic differential equations. Approximation and associated nonlinear PDEs, J. Math. Anal. Appl., 413 (2014), 47-68.
doi: 10.1016/j.jmaa.2013.11.028. |
[10] |
Z. Li and J. Luo, Mean-field reflected backward stochastic differential equations, Stat. Probab. Lett., 82 (2012), 1961-1968.
doi: 10.1016/j.spl.2012.06.018. |
[11] |
J. Yan, S. Peng and S. Fang, BSDE and stochastic optimizations, in Topics in Stochastic Analysis (eds. L. Wu), Science Press, 1997 (In Chinese). |
show all references
References:
[1] |
G. Barles, R. Buckdahn and E. Pardoux, Backward stochastic differential equations and integral-partial differential equations, Stoch. Stoch. Rep., 60 (1997), 57-83.
doi: 10.1080/17442509708834099. |
[2] |
R. Buckdahn and J. Li, Stochastic differential games and viscosity solutions of Hamilton- Jacobi-Bellman-Isaacs equations, SIAM. J. Control. Optim., 47 (2008), 444-475.
doi: 10.1137/060671954. |
[3] |
R. Buckdahn and J. Li, Stochastic differential games with reflection and related obstacle problems for Isaacs equations, Acta Math. Appl. Sin.-Enql. Ser., 27 (2011), 647-678.
doi: 10.1007/s10255-011-0068-8. |
[4] |
R. Buckdahn, B. Djehiche, J. Li and S. Peng, Mean-field backward stochastic differential equations. A limit approach, Ann. Probab., 37 (2009), 1524-1565.
doi: 10.1214/08-AOP442. |
[5] |
R. Buckdahn, J. Li and S. Peng, Mean-field backward stochastic differential equations and related partial differential equations, Stoch. Proc. App., 119 (2009), 3133-3154.
doi: 10.1016/j.spa.2009.05.002. |
[6] |
M. G. Crandall, H. Ishii and P. L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27 (1992), 1-67.
doi: 10.1090/S0273-0979-1992-00266-5. |
[7] |
T. Hao and J. Li, Backward stochastic differential equations coupled with value function and related optimal control problems, Abstract Appl. Anal., 2014 (2014), Art. ID 262713, 17 pp.
doi: 10.1155/2014/262713. |
[8] |
N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng and M. C. Quenez, Reflected solutions of backward SDE's, and related obstacle problems for PDE's, Ann. Probab., 25 (1997), 702-737.
doi: 10.1214/aop/1024404416. |
[9] |
J. Li, Reflected mean-field backward stochastic differential equations. Approximation and associated nonlinear PDEs, J. Math. Anal. Appl., 413 (2014), 47-68.
doi: 10.1016/j.jmaa.2013.11.028. |
[10] |
Z. Li and J. Luo, Mean-field reflected backward stochastic differential equations, Stat. Probab. Lett., 82 (2012), 1961-1968.
doi: 10.1016/j.spl.2012.06.018. |
[11] |
J. Yan, S. Peng and S. Fang, BSDE and stochastic optimizations, in Topics in Stochastic Analysis (eds. L. Wu), Science Press, 1997 (In Chinese). |
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