
Previous Article
Portfolio theory for squared returns correlated across time
 PUQR Home
 This Issue

Next Article
Pathwise noarbitrage in a class of Delta hedging strategies
Meanfield stochastic linear quadratic optimal control problems: closedloop solvability
1 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China; 
2 Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA 
References:
[1] 
Ait Rami, M, Moore, JB, Zhou, XY:Indefinite stochastic linear quadratic control and generalized differential Riccati equation. SIAM J. Control Optim 40, 12961311 (2001), 
[2] 
Andersson, D, Djehiche, B:A maximum principle for SDEs of meanfield type. Appl. Math. Optim 63, 341356 (2011), 
[3] 
Athans, M:The matrix minimum principle. Inform. Control 11, 592606 (1968), 
[4] 
Buckdahn, R, Djehiche, B, Li, J:A general stochastic maximum principle for SDEs of meanfield type.Appl. Math. Optim 64, 197216 (2011), 
[5] 
Buckdahn, R, Djehiche, B, Li, J, Peng, S:Meanfield backward stochastic differential equations:a limit approach. Ann. Probab 37, 15241565 (2009), 
[6] 
Buckdahn, R, Li, J, Peng, S:Meanfield backward stochastic differential equations and related partial differential equations. Stoch. Proc. Appl 119, 31333154 (2009), 
[7] 
Chen, S, Li, X, Zhou, XY:Stochastic linear quadratic regulators with indefinite control weight costs.SIAM J. Control Optim 36, 16851702 (1998), 
[8] 
Chen, S, Yong, J:Stochastic linear quadratic optimal control problems with random coefficients. Chin.Ann. Math 21B, 323338 (2000), 
[9] 
Cui, XY, Li, X, Li, D:Unified framework of meanfield formulations for optimal multiperiod meanvariance portfolio selection. IEEE Trans. Auto. Control 59, 18331844 (2014), 
[10] 
Elliott, R, Li, X, Ni, YH:Discrete time meanfield stochastic linearquadratic optimal control problems.Automatica 49, 32223233 (2013), 
[11] 
Huang, J, Li, X, Wang, TX:Meanfield linearquadraticGaussian (LQG) games for stochastic integral systems. IEEE Trans. Auto. Control (2015). doi:10.1109/TAC.2015.2506620, 
[12] 
Huang, J, Li, X, Yong, J:A linearquadratic optimal control problem for meanfield stochastic differential equations in infinite horizon. Math. Control Related Fields 5, 97139 (2015), 
[13] 
Kac, M:Foundations of kinetic theory. Proc. Third Berkeley Symp. Math. Stat. Probab 3, 171197 (1956), 
[14] 
McKean, HP:A class of Markov processes associated with nonlinear parabolic equations. Proc. Natl.Acad. Sci. USA 56, 19071911 (1966), 
[15] 
MeyerBrandis, T, Øksendal, B, Zhou, XY:A meanfield stochastic maximum principle via Malliavin calculus. Stochastics 84(56), 643666 (2012). doi:10.1080/17442508.2011.651619, 
[16] 
Penrose, R:A generalized inverse of matrices. Proc. Cambridge Philos Soc 52, 1719 (1955), 
[17] 
Sun, J:Meanfield stochastic linear quadratic optimal control problems:openloop solvabilities. ESAIM:COCV, 016023 (2016). doi:10.1051/cocv/2, 
[18] 
Sun, J, Yong, J:Linear quadratic stochastic differential games:openloop and closedloop saddle points.SIAM J. Control Optim 52, 40824121 (2014), 
[19] 
Sun, J, Yong, J, Zhang, S:Linear quadratic stochastic twoperson zerosum differential games in an infinite horizon. ESAIM COCV 22, 743769 (2016). doi:10.1051/cocv/2015024, 
[20] 
Tang, S:General linear quadratic optimal stochastic control problems with random coefficients:linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM J. Control Optim 42, 5375 (2003), 
[21] 
Wonham, WM:On a matrix Riccati equation of stochastic control. SIAM J. Control Optim 6, 681697(1968), 
[22] 
Yong, J:Linearquadratic optimal control problems for meanfield stochastic differential equations. SIAM J. Control Optim 51, 28092838 (2013), 
[23] 
Yong, J, Zhou, XY:Stochastic controls:Hamiltonian systems and HJB equations. SpringerVerlag, New York (1999), 
show all references
References:
[1] 
Ait Rami, M, Moore, JB, Zhou, XY:Indefinite stochastic linear quadratic control and generalized differential Riccati equation. SIAM J. Control Optim 40, 12961311 (2001), 
[2] 
Andersson, D, Djehiche, B:A maximum principle for SDEs of meanfield type. Appl. Math. Optim 63, 341356 (2011), 
[3] 
Athans, M:The matrix minimum principle. Inform. Control 11, 592606 (1968), 
[4] 
Buckdahn, R, Djehiche, B, Li, J:A general stochastic maximum principle for SDEs of meanfield type.Appl. Math. Optim 64, 197216 (2011), 
[5] 
Buckdahn, R, Djehiche, B, Li, J, Peng, S:Meanfield backward stochastic differential equations:a limit approach. Ann. Probab 37, 15241565 (2009), 
[6] 
Buckdahn, R, Li, J, Peng, S:Meanfield backward stochastic differential equations and related partial differential equations. Stoch. Proc. Appl 119, 31333154 (2009), 
[7] 
Chen, S, Li, X, Zhou, XY:Stochastic linear quadratic regulators with indefinite control weight costs.SIAM J. Control Optim 36, 16851702 (1998), 
[8] 
Chen, S, Yong, J:Stochastic linear quadratic optimal control problems with random coefficients. Chin.Ann. Math 21B, 323338 (2000), 
[9] 
Cui, XY, Li, X, Li, D:Unified framework of meanfield formulations for optimal multiperiod meanvariance portfolio selection. IEEE Trans. Auto. Control 59, 18331844 (2014), 
[10] 
Elliott, R, Li, X, Ni, YH:Discrete time meanfield stochastic linearquadratic optimal control problems.Automatica 49, 32223233 (2013), 
[11] 
Huang, J, Li, X, Wang, TX:Meanfield linearquadraticGaussian (LQG) games for stochastic integral systems. IEEE Trans. Auto. Control (2015). doi:10.1109/TAC.2015.2506620, 
[12] 
Huang, J, Li, X, Yong, J:A linearquadratic optimal control problem for meanfield stochastic differential equations in infinite horizon. Math. Control Related Fields 5, 97139 (2015), 
[13] 
Kac, M:Foundations of kinetic theory. Proc. Third Berkeley Symp. Math. Stat. Probab 3, 171197 (1956), 
[14] 
McKean, HP:A class of Markov processes associated with nonlinear parabolic equations. Proc. Natl.Acad. Sci. USA 56, 19071911 (1966), 
[15] 
MeyerBrandis, T, Øksendal, B, Zhou, XY:A meanfield stochastic maximum principle via Malliavin calculus. Stochastics 84(56), 643666 (2012). doi:10.1080/17442508.2011.651619, 
[16] 
Penrose, R:A generalized inverse of matrices. Proc. Cambridge Philos Soc 52, 1719 (1955), 
[17] 
Sun, J:Meanfield stochastic linear quadratic optimal control problems:openloop solvabilities. ESAIM:COCV, 016023 (2016). doi:10.1051/cocv/2, 
[18] 
Sun, J, Yong, J:Linear quadratic stochastic differential games:openloop and closedloop saddle points.SIAM J. Control Optim 52, 40824121 (2014), 
[19] 
Sun, J, Yong, J, Zhang, S:Linear quadratic stochastic twoperson zerosum differential games in an infinite horizon. ESAIM COCV 22, 743769 (2016). doi:10.1051/cocv/2015024, 
[20] 
Tang, S:General linear quadratic optimal stochastic control problems with random coefficients:linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM J. Control Optim 42, 5375 (2003), 
[21] 
Wonham, WM:On a matrix Riccati equation of stochastic control. SIAM J. Control Optim 6, 681697(1968), 
[22] 
Yong, J:Linearquadratic optimal control problems for meanfield stochastic differential equations. SIAM J. Control Optim 51, 28092838 (2013), 
[23] 
Yong, J, Zhou, XY:Stochastic controls:Hamiltonian systems and HJB equations. SpringerVerlag, New York (1999), 
[1] 
Jingrui Sun, Hanxiao Wang. Meanfield stochastic linearquadratic optimal control problems: Weak closedloop solvability. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020026 
[2] 
Hanxiao Wang, Jingrui Sun, Jiongmin Yong. Weak closedloop solvability of stochastic linearquadratic optimal control problems. Discrete & Continuous Dynamical Systems  A, doi: 10.3934/dcds.2019117 
[3] 
Jianhui Huang, Xun Li, Jiongmin Yong. A linearquadratic optimal control problem for meanfield stochastic differential equations in infinite horizon. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2015.5.97 
[4] 
Nguyen Thi Hoai. Asymptotic approximation to a solution of a singularly perturbed linearquadratic optimal control problem with secondorder linear ordinary differential equation of state variable. Numerical Algebra, Control & Optimization, 2020 doi: 10.3934/naco.2020040 
[5] 
Kai Du, Jianhui Huang, Zhen Wu. Linear quadratic meanfieldgame of backward stochastic differential systems. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2018028 
[6] 
Tianxiao Wang. Characterizations of equilibrium controls in time inconsistent meanfield stochastic linear quadratic problems. I. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2019018 
[7] 
Alain Bensoussan, Shaokuan Chen, Suresh P. Sethi. Linear quadratic differential games with mixed leadership: The openloop solution. Numerical Algebra, Control & Optimization, doi: 10.3934/naco.2013.3.95 
[8] 
Michael Herty, Lorenzo Pareschi, Sonja Steffensen. Meanfield control and Riccati equations. Networks & Heterogeneous Media, doi: 10.3934/nhm.2015.10.699 
[9] 
Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, doi: 10.3934/proc.2013.2013.437 
[10] 
Jianhui Huang, Shujun Wang, Zhen Wu. Backwardforward linearquadratic meanfield games with major and minor agents. Probability, Uncertainty and Quantitative Risk, doi: 10.1186/s4154601600099 
[11] 
Haiyan Zhang. A necessary condition for meanfield type stochastic differential equations with correlated state and observation noises. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2016.12.1287 
[12] 
Juan Li, Wenqiang Li. Controlled reflected meanfield backward stochastic differential equations coupled with value function and related PDEs. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2015.5.501 
[13] 
Hancheng Guo, Jie Xiong. A secondorder stochastic maximum principle for generalized meanfield singular control problem. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2018018 
[14] 
Pasquale Palumbo, Pierdomenico Pepe, Simona Panunzi, Andrea De Gaetano. Robust closedloop control of plasma glycemia: A discretedelay model approach. Discrete & Continuous Dynamical Systems  B, doi: 10.3934/dcdsb.2009.12.455 
[15] 
Filippo Cacace, Valerio Cusimano, Alfredo Germani, Pasquale Palumbo, Federico Papa. Closedloop control of tumor growth by means of antiangiogenic administration. Mathematical Biosciences & Engineering, doi: 10.3934/mbe.2018037 
[16] 
Xiaochen Sun, Fei Hu, Yancong Zhou, ChengChew Lim. Optimal acquisition, inventory and production decisions for a closedloop manufacturing system with legislation constraint. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2015.11.1355 
[17] 
Salah Eddine Choutri, Boualem Djehiche, Hamidou Tembine. Optimal control and zerosum games for Markov chains of meanfield type. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2019026 
[18] 
Adel Chala, Dahbia Hafayed. On stochastic maximum principle for risksensitive of fully coupled forwardbackward stochastic control of meanfield type with application. Evolution Equations & Control Theory, doi: 10.3934/eect.2020035 
[19] 
Rong Yang, Li Chen. Meanfield limit for a collisionavoiding flocking system and the timeasymptotic flocking dynamics for the kinetic equation. Kinetic & Related Models, doi: 10.3934/krm.2014.7.381 
[20] 
Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Meanfield backward stochastic Volterra integral equations. Discrete & Continuous Dynamical Systems  B, doi: 10.3934/dcdsb.2013.18.1929 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]