Backward-forward linear-quadratic mean-field games with major and minor agents

Jian Huang1, Shujun Wang2, Zhen Wu2
1Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China
2School of Mathematics, Shandong University, Jinan, China

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Tài liệu tham khảo

Andersson, D, Djehiche, B: A maximum principle for SDEs of mean-field type, Appl. Math. Optim. 63, 341–356 (2011).

Antonelli, F: Backward-forward stochastic differential equations. Ann. Appl. Probab. 3, 777–793 (1993).

Bardi, M: Explicit solutions of some linear-quadratic mean field games. Netw. Heterog. Media. 7, 243–261 (2012).

Bensoussan, A, Sung, K, Yam, S, Yung, S: Linear-quadratic mean-field games. J. Optim. Theory Appl. 169, 496–529 (2016).

Bismut, J: An introductory approach to duality in optimal stochastic control. SIAM Rev. 20, 62–78 (1978).

Buckdahn, R, Cardaliaguet, P, Quincampoix, M: Some recent aspects of differential game theory. Dynam Games Appl. 1, 74–114 (2010).

Buckdahn, R, Djehiche, B, Li, J: A general stochastic maximum principle for SDEs of mean-field type. Appl. Math. Optim. 64, 197–216 (2011).

Buckdahn, R, Djehiche, B, Li, J, Peng, S: Mean-field backward stochastic differential equations: a limit approach. Ann. Probab. 37, 1524–1565 (2009a).

Buckdahn, R, Li, J, Peng, S: Mean-field backward stochastic differential equations and related partial differential equations, Stoch. Process. Appl. 119, 3133–3154 (2009b).

Buckdahn, R, Li, J, Peng, S: Nonlinear stochastic differential games involving a major player and a large number of collectively acting minor agents. SIAM J. Control Optim. 52, 451–492 (2014).

Carmona, R, Delarue, F: Probabilistic analysis of mean-field games. SIAM J. Control Optim. 51, 2705–2734 (2013).

Cvitanić, J, Ma, J: Hedging options for a large investor and forward-backward SDE’s. Ann. Appl. Probab. 6, 370–398 (1996).

Duffie, D, Epstein, L: Stochastic differential utility. Econometrica. 60, 353–394 (1992).

El Karoui, N, Peng, S, Quenez, M: Backward stochastic differential equations in finance. Math.Finance. 7, 1–71 (1997).

Espinosa, G, Touzi, N: Optimal investment under relative performance concerns. Math. Finance. 25, 221–257 (2015).

Guéant, O, Lasry, J-M, Lions, P-L: Mean field games and applications, Paris-Princeton lectures on mathematical finance. Springer, Berlin (2010).

Huang, M: Large-population LQG games involving a major player: the Nash certainty equivalence principle. SIAM J. Control Optim. 48, 3318–3353 (2010).

Huang, M, Caines, P, Malhamé, R: Large-population cost-coupled LQG problems with non-uniform agents: individual-mass behavior and decentralized ε-Nash equilibria. IEEE Trans. Autom. Control. 52, 1560–1571 (2007).

Huang, M, Caines, P, Malhamé, R: Social optima in mean field LQG control: centralized and decentralized strategies. IEEE Trans. Autom. Control. 57, 1736–1751 (2012).

Huang, M, Malhamé, R, Caines, P: Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6, 221–251 (2006).

Hu, Y, Peng, S: Solution of forwardbackward stochastic differential equations. Proba. Theory Rel. Fields. 103, 273–283 (1995).

Lasry, J-M, Lions, P-L: Mean field games. Japan J. Math. 2, 229–260 (2007).

Li, T, Zhang, J: Asymptotically optimal decentralized control for large population stochastic multiagent systems. IEEE Trans. Autom. Control. 53, 1643–1660 (2008).

Lim, E, Zhou, XY: Linear-quadratic control of backward stochastic differential equations. SIAM J. Control Optim. 40, 450–474 (2001).

Ma, J, Protter, P, Yong, J: Solving forward-backward stochastic differential equations explicitly-a four step scheme, Proba. Theory Rel. Fields. 98, 339–359 (1994).

Ma, J, Wu, Z, Zhang, D, Zhang, J: On well-posedness of forward-backward SDEs-a unified approach. Ann. Appl. Probab. 25, 2168–2214 (2015).

Ma, J, Yong, J: Forward-Backward Stochastic Differential Equations and Their Applications. Springer-Verlag, Berlin Heidelberg (1999).

Nguyen, S, Huang, M: Linear-quadratic-Gaussian mixed games with continuum-parametrized minor players. SIAM J. Control Optim. 50, 2907–2937 (2012).

Nourian, M, Caines, P: ε-Nash mean field game theory for nonlinear stochastic dynamical systems with major and minor agents. SIAM J. Control Optim. 51, 3302–3331 (2013).

Pardoux, E, Peng, S: Adapted solution of backward stochastic equation. Syst. Control Lett. 14, 55–61 (1990).

Peng, S, Wu, Z: Fully coupled forward-backward stochastic differential equations and applications to optimal control, SIAM. J. Control Optim. 37, 825–843 (1999).

Wang, G, Wu, Z: The maximum principles for stochastic recursive optimal control problems under partial information. IEEE Trans. Autom. Control. 54, 1230–1242 (2009).

Wu, Z: A general maximum principle for optimal control of forward-backward stochastic systems. Automatica. 49, 1473–1480 (2013).

Yong, J: Finding adapted solutions of forward-backward stochastic differential equations: method of continuation. Proba. Theory Rel. Fields. 107, 537–572 (1997).

Yong, J: Optimality variational principle for controlled forward-backward stochastic differential equations with mixed initial-terminal conditions. SIAM J. Control Optim. 48, 4119–4156 (2010).

Yong, J, Zhou, XY: Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer-Verlag, New York (1999).

Yu, Z: Linear-quadratic optimal control and nonzero-sum differential game of forward-backward stochastic system. Asian J.Control. 14, 173–185 (2012).