Tao HAO
,
Juan LI
. BSDES IN GAMES, COUPLED WITH THE VALUE FUNCTIONS. ASSOCIATED NONLOCAL BELLMAN-ISAACS EQUATIONS[J]. Acta mathematica scientia, Series B, 2017
, 37(5)
: 1497
-1518
.
DOI: 10.1016/S0252-9602(17)30087-5
[1] Andersson D, Djehiche B. A maximum principle for SDEs of mean-field type. Appl Math Optim, 2011, 63(3):341-356
[2] Bayraktar E, Poor H V. Stochastic differential games in a non-Markovian setting. SIAM J Control Optim, 2005, 43(5):1737-1756
[3] Bossy M. Some stochastic particle methods for nonlinear parabolic PDEs. ESAIM:Proc, 2005, 15:18-57
[4] Bossy M, Talay D. A stochastic particle method for the McKean-Vlasov and the Burgers equation. Math Comput, 1997, 66(217):157-192
[5] Browne S. Stochastic differential portfolio games. J Appl Probab, 2000, 37(1):126-147
[6] Buckdahn R, Cardaliaguet P, Rainer C. Nash equilibrium payoffs for nonzero-sum stochastic differential games. SIAM J Control Optim, 2004, 43(2):624-642
[7] Buckdahn R, Djehiche B, Li J. A general stochastic maximum principle for SDEs of mean-field type. Appl Math Optim, 2011, 64(2):197-216
[8] Buckdahn R, Djehiche B, Li J, Peng S. Mean-field backward stochastic differential equations:a limit approach. Ann Probab, 2009, 37(4):1524-1565
[9] Buckdahn R, Li J. Stochastic differential games and viscosity solutions of Hamilton-Jacobi-Bellman-Isaacs equations. SIAM J Control Optim, 2008, 47(1):444-475
[10] Buckdahn R, Li J, Peng S. Mean-field backward stochastic differential equations and related partial differential equations. Stoch Proc Appl, 2009, 119(10):3133-3154
[11] Chan T. Dynamics of the McKean-Vlasov equation. Ann Probab, 1994, 22(1):431-441
[12] Crandall M G, Ishii H, Lions P L. User's guide to viscosity solutions of second order partial differential equations. Bull Amer Math Soc, 1992, 27(1):1-67
[13] Fleming W H, Souganidis P E. On the existence of value functions of two-player, zero-sum stochastic differential games. Indiana Univ Math J, 1989, 38(2):293-314
[14] Hao T, Li J. Backward stochastic differential equations coupled with value function and related optimal control problems. Abstr Appl Analysis, 2014, 2014, 17 pages, article ID 262713
[15] El Karoui N, Peng S, Quenez M C. Backward stochastic differential equations in finance. Math Finance, 1997, 7(1):1-71
[16] Ikeda N, Watanabe S. Stochastic Differential Equations and Diffusion Processes. Tokyo:North HollandKodansha, 1989
[17] Karatzas I, Shreve S E. Brownian Motion and Stochastic Calculus. New York:Springer, 1987
[18] Kotelenez P. A class of quasilinear stochastic partial differential equations of McKean-Vlasov type with mass conservation. Probab Theory Rel Fields, 1995, 102(2):159-188
[19] Li J. Stochastic maximum principle in the mean-field controls. Automatica, 2012, 48(2):366-373
[20] Pardoux E. BSDEs, weak convergence and homogenization of semilinear PDEs. Nonl Analysis Diff Equ Control, 1999, 528:503-549
[21] Pardoux E, Peng S. Adapted solution of a backward stochastic differential equation. Syst Control Lett, 1990, 14(1):55-61
[22] Peng S. Probabilistic interpretation for systems of quasilinear parabolic partial differential equations. Stoch Stoch Rep, 1991, 37(1/2):61-74
[23] Peng S. Backward stochastic differential equations-stochastic optimization theory and viscosity solutions of HJB equations//Yan J A, Peng S G, Fang S Z, Wu L M. Topics on Stochastic Analysis. Beijing:Science Press, 1997:85-138(in Chinese)
[24] Pra P D, Hollander F D. McKean-Vlasov limit for interacting random processes in random media. J Stat Phys, 1996, 84(3/4):735-772
[25] Talay D, Vaillant O. A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations. Ann Appl Probab, 2003, 13(1):140-180
