Fully-coupled mean-field FBSDE and maximum principle for related optimal control problem

[1]  Zhanghua Wu,et al.  Linear-Quadratic Large-Population Problem with Partial Information: Hamiltonian Approach and Riccati Approach , 2022, SIAM J. Control. Optim..

[2]  Mao Fabrice Djete,et al.  McKean–Vlasov optimal control: The dynamic programming principle , 2019, The Annals of Probability.

[3]  Qingxin Meng,et al.  A global maximum principle for optimal control of general mean-field forward-backward stochastic systems with jumps , 2018, ESAIM: Control, Optimisation and Calculus of Variations.

[4]  Beatrice Acciaio,et al.  Extended Mean Field Control Problems: Stochastic Maximum Principle and Transport Perspective , 2018, SIAM J. Control. Optim..

[5]  Tzu-Wei Yang,et al.  Forward–backward stochastic differential equations with monotone functionals and mean field games with common noise , 2016, Stochastic Processes and their Applications.

[6]  Ying Hu,et al.  Linear-Quadratic-Gaussian Mixed Mean-Field Games with Heterogeneous Input Constraints , 2017, SIAM J. Control. Optim..

[7]  Huyên Pham,et al.  Dynamic Programming for Optimal Control of Stochastic McKean-Vlasov Dynamics , 2016, SIAM J. Control. Optim..

[8]  Jin Ma,et al.  A Stochastic Maximum Principle for General Mean-Field Systems , 2016 .

[9]  H. Pham,et al.  Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics , 2016, 1606.08204.

[10]  Olivier Pironneau,et al.  Dynamic Programming for Mean-Field Type Control , 2014, Journal of Optimization Theory and Applications.

[11]  H. Pham,et al.  Bellman equation and viscosity solutions for mean-field stochastic control problem , 2015, 1512.07866.

[12]  Alain Bensoussan,et al.  Well-posedness of mean-field type forward–backward stochastic differential equations , 2015 .

[13]  Suresh P. Sethi,et al.  The Maximum Principle for Global Solutions of Stochastic Stackelberg Differential Games , 2012, SIAM J. Control. Optim..

[14]  R. Carmona,et al.  Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics , 2013, 1303.5835.

[15]  Rene Carmona,et al.  Mean field forward-backward stochastic differential equations , 2012, 1211.4186.

[16]  R. Carmona,et al.  Control of McKean–Vlasov dynamics versus mean field games , 2012, 1210.5771.

[17]  Zhen Wu,et al.  On well-posedness of forward-backward SDEs-A unified approach , 2011, 1110.4658.

[18]  Daniel Andersson,et al.  A Maximum Principle for SDEs of Mean-Field Type , 2011 .

[19]  Boualem Djehiche,et al.  Mean-Field Backward Stochastic Differential Equations . A Limit Approach ∗ , 2007 .

[20]  S. Peng,et al.  Mean-field backward stochastic differential equations and related partial differential equations , 2007, 0711.2167.

[21]  P. Lions,et al.  Mean field games , 2007 .

[22]  Peter E. Caines,et al.  Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle , 2006, Commun. Inf. Syst..

[23]  F. Delarue On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case , 2002 .

[24]  Jiongmin Yong,et al.  A Leader-Follower Stochastic Linear Quadratic Differential Game , 2002, SIAM J. Control. Optim..

[25]  É. Pardoux,et al.  Forward-backward stochastic differential equations and quasilinear parabolic PDEs , 1999 .

[26]  S. Peng,et al.  Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control , 1999 .

[27]  T. Başar,et al.  Dynamic Noncooperative Game Theory, 2nd Edition , 1998 .

[28]  R. Darling,et al.  BACKWARDS SDE WITH RANDOM TERMINAL TIME AND APPLICATIONS TO SEMILINEAR ELLIPTIC PDE , 1997 .

[29]  J. Yong Finding adapted solutions of forward–backward stochastic differential equations: method of continuation , 1997 .

[30]  S. Peng,et al.  Solution of forward-backward stochastic differential equations , 1995 .

[31]  J. Yong,et al.  Solving forward-backward stochastic differential equations explicitly — a four step scheme , 1994 .

[32]  F. Antonelli,et al.  Backward-Forward Stochastic Differential Equations , 1993 .

[33]  Shige Peng,et al.  Probabilistic interpretation for systems of quasilinear parabolic partial differential equations , 1991 .

[34]  A. Sznitman Topics in propagation of chaos , 1991 .

[35]  S. Peng,et al.  Adapted solution of a backward stochastic differential equation , 1990 .

[36]  T. Başar,et al.  Stackelberg strategies in linear-quadratic stochastic differential games , 1981 .

[37]  J. Bismut Conjugate convex functions in optimal stochastic control , 1973 .

[38]  J. Cruz,et al.  On the Stackelberg strategy in nonzero-sum games , 1973 .

[39]  J. B. Cruz,et al.  Additional aspects of the Stackelberg strategy in nonzero-sum games , 1972, IEEE Conference on Decision and Control.

[40]  C. Chen,et al.  Stackelburg solution for two-person games with biased information patterns , 1972 .

[41]  H. Stackelberg,et al.  Marktform und Gleichgewicht , 1935 .