Well-posedness of mean-field type forward-backward stochastic differential equations

Stochastic Processes and their Applications

Volumn 125, Issue 9, 2015, Pages 3327-3354

  Bensoussan, A ^a,b   Yam, S C P ^c   Zhang, Z ^c  

^a UNIVERSITY OF TEXAS AT DALLAS   (United States)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Forward backward stochastic differential equations; Linear quadratic setting; Mean field type; Monotonicity conditions; Well posedness

Indexed keywords

ABSTRACTING; DIFFERENTIAL EQUATIONS;

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS; LINEAR QUADRATIC; MEAN FIELD; MONOTONICITY CONDITIONS; WELLPOSEDNESS;

STOCHASTIC SYSTEMS;

EID: 84929614856     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2015.04.006     Document Type: Article

References (11)

1. A. Bensoussan, J. Frehse, and S.C.P. Yam Mean Field Games and Mean Field Type Control Theory Springer Briefs in Mathematics 2013
2. A. Bensoussan, K.C.J. Sung, S.C.P Yam, S.P. Yung, Linear-quadratic mean field games, arXiv preprint arXiv: 1404.5714 (2014).
3. R. Buckdahn, B. Djehiche, J. Li, and S. Peng Mean-field backward stochastic differential equations: a limit approach Ann. Probab. 37 4 2009 1524 1565
4. R. Carmona, and F. Delarue Mean field forward-backward stochastic differential equations Electron. Commun. Probab. 18 2013 Article 68
5. R. Carmona, F. Delarue, Forward-backward stochastic differential equations and controlled McKean Vlasov dynamics, arXiv preprint arXiv:1303.5835.
6. R. Carmona, and F. Delarue Probabilistic analysis of mean-field games SIAM J. Control Optim. 51 4 2013 2705 2734
7. F. Delarue On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case Stoch. Process Appl. 99 2 2002 209 286
8. Y. Hu, and S. Peng Solution of forward-backward stochastic differential equations Probab. Theory Related Fields 103 1995 273 283
9. J. Ma, P. Protter, and J. Yong Solving forward-backward stochastic differential equations explicitly - a four step scheme Probab. Theory Related Fields 98 1994 339 359
10. E. Pardoux, and S. Tang Forward-backward stochastic differential equations and quasilinear PDEs Probab. Theory Related Fields 114 1999 123 150
11. S. Peng, and Z. Wu Fully coupled forward-backward stochastic differential equations and applications to optimal control SIAM J. Control Optim. 37 1996 825 843