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Mean-field stochastic linear quadratic optimal control problems: closed-loop 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, 1296-1311 (2001) Google Scholar |
[2] |
Andersson, D, Djehiche, B:A maximum principle for SDEs of mean-field type. Appl. Math. Optim 63, 341-356 (2011) Google Scholar |
[3] |
Athans, M:The matrix minimum principle. Inform. Control 11, 592-606 (1968) Google Scholar |
[4] |
Buckdahn, R, Djehiche, B, Li, J:A general stochastic maximum principle for SDEs of mean-field type.Appl. Math. Optim 64, 197-216 (2011) Google Scholar |
[5] |
Buckdahn, R, Djehiche, B, Li, J, Peng, S:Mean-field backward stochastic differential equations:a limit approach. Ann. Probab 37, 1524-1565 (2009) Google Scholar |
[6] |
Buckdahn, R, Li, J, Peng, S:Mean-field backward stochastic differential equations and related partial differential equations. Stoch. Proc. Appl 119, 3133-3154 (2009) Google Scholar |
[7] |
Chen, S, Li, X, Zhou, XY:Stochastic linear quadratic regulators with indefinite control weight costs.SIAM J. Control Optim 36, 1685-1702 (1998) Google Scholar |
[8] |
Chen, S, Yong, J:Stochastic linear quadratic optimal control problems with random coefficients. Chin.Ann. Math 21B, 323-338 (2000) Google Scholar |
[9] |
Cui, XY, Li, X, Li, D:Unified framework of mean-field formulations for optimal multi-period meanvariance portfolio selection. IEEE Trans. Auto. Control 59, 1833-1844 (2014) Google Scholar |
[10] |
Elliott, R, Li, X, Ni, YH:Discrete time mean-field stochastic linear-quadratic optimal control problems.Automatica 49, 3222-3233 (2013) Google Scholar |
[11] |
Huang, J, Li, X, Wang, TX:Mean-field linear-quadratic-Gaussian (LQG) games for stochastic integral systems. IEEE Trans. Auto. Control (2015). doi:10.1109/TAC.2015.2506620 Google Scholar |
[12] |
Huang, J, Li, X, Yong, J:A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon. Math. Control Related Fields 5, 97-139 (2015) Google Scholar |
[13] |
Kac, M:Foundations of kinetic theory. Proc. Third Berkeley Symp. Math. Stat. Probab 3, 171-197 (1956) Google Scholar |
[14] |
McKean, HP:A class of Markov processes associated with nonlinear parabolic equations. Proc. Natl.Acad. Sci. USA 56, 1907-1911 (1966) Google Scholar |
[15] |
Meyer-Brandis, T, Øksendal, B, Zhou, XY:A mean-field stochastic maximum principle via Malliavin calculus. Stochastics 84(5-6), 643-666 (2012). doi:10.1080/17442508.2011.651619 Google Scholar |
[16] |
Penrose, R:A generalized inverse of matrices. Proc. Cambridge Philos Soc 52, 17-19 (1955) Google Scholar |
[17] |
Sun, J:Mean-field stochastic linear quadratic optimal control problems:open-loop solvabilities. ESAIM:COCV, 016023 (2016). doi:10.1051/cocv/2 Google Scholar |
[18] |
Sun, J, Yong, J:Linear quadratic stochastic differential games:open-loop and closed-loop saddle points.SIAM J. Control Optim 52, 4082-4121 (2014) Google Scholar |
[19] |
Sun, J, Yong, J, Zhang, S:Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon. ESAIM COCV 22, 743-769 (2016). doi:10.1051/cocv/2015024 Google Scholar |
[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, 53-75 (2003) Google Scholar |
[21] |
Wonham, WM:On a matrix Riccati equation of stochastic control. SIAM J. Control Optim 6, 681-697(1968) Google Scholar |
[22] |
Yong, J:Linear-quadratic optimal control problems for mean-field stochastic differential equations. SIAM J. Control Optim 51, 2809-2838 (2013) Google Scholar |
[23] |
Yong, J, Zhou, XY:Stochastic controls:Hamiltonian systems and HJB equations. Springer-Verlag, New York (1999) Google Scholar |
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, 1296-1311 (2001) Google Scholar |
[2] |
Andersson, D, Djehiche, B:A maximum principle for SDEs of mean-field type. Appl. Math. Optim 63, 341-356 (2011) Google Scholar |
[3] |
Athans, M:The matrix minimum principle. Inform. Control 11, 592-606 (1968) Google Scholar |
[4] |
Buckdahn, R, Djehiche, B, Li, J:A general stochastic maximum principle for SDEs of mean-field type.Appl. Math. Optim 64, 197-216 (2011) Google Scholar |
[5] |
Buckdahn, R, Djehiche, B, Li, J, Peng, S:Mean-field backward stochastic differential equations:a limit approach. Ann. Probab 37, 1524-1565 (2009) Google Scholar |
[6] |
Buckdahn, R, Li, J, Peng, S:Mean-field backward stochastic differential equations and related partial differential equations. Stoch. Proc. Appl 119, 3133-3154 (2009) Google Scholar |
[7] |
Chen, S, Li, X, Zhou, XY:Stochastic linear quadratic regulators with indefinite control weight costs.SIAM J. Control Optim 36, 1685-1702 (1998) Google Scholar |
[8] |
Chen, S, Yong, J:Stochastic linear quadratic optimal control problems with random coefficients. Chin.Ann. Math 21B, 323-338 (2000) Google Scholar |
[9] |
Cui, XY, Li, X, Li, D:Unified framework of mean-field formulations for optimal multi-period meanvariance portfolio selection. IEEE Trans. Auto. Control 59, 1833-1844 (2014) Google Scholar |
[10] |
Elliott, R, Li, X, Ni, YH:Discrete time mean-field stochastic linear-quadratic optimal control problems.Automatica 49, 3222-3233 (2013) Google Scholar |
[11] |
Huang, J, Li, X, Wang, TX:Mean-field linear-quadratic-Gaussian (LQG) games for stochastic integral systems. IEEE Trans. Auto. Control (2015). doi:10.1109/TAC.2015.2506620 Google Scholar |
[12] |
Huang, J, Li, X, Yong, J:A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon. Math. Control Related Fields 5, 97-139 (2015) Google Scholar |
[13] |
Kac, M:Foundations of kinetic theory. Proc. Third Berkeley Symp. Math. Stat. Probab 3, 171-197 (1956) Google Scholar |
[14] |
McKean, HP:A class of Markov processes associated with nonlinear parabolic equations. Proc. Natl.Acad. Sci. USA 56, 1907-1911 (1966) Google Scholar |
[15] |
Meyer-Brandis, T, Øksendal, B, Zhou, XY:A mean-field stochastic maximum principle via Malliavin calculus. Stochastics 84(5-6), 643-666 (2012). doi:10.1080/17442508.2011.651619 Google Scholar |
[16] |
Penrose, R:A generalized inverse of matrices. Proc. Cambridge Philos Soc 52, 17-19 (1955) Google Scholar |
[17] |
Sun, J:Mean-field stochastic linear quadratic optimal control problems:open-loop solvabilities. ESAIM:COCV, 016023 (2016). doi:10.1051/cocv/2 Google Scholar |
[18] |
Sun, J, Yong, J:Linear quadratic stochastic differential games:open-loop and closed-loop saddle points.SIAM J. Control Optim 52, 4082-4121 (2014) Google Scholar |
[19] |
Sun, J, Yong, J, Zhang, S:Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon. ESAIM COCV 22, 743-769 (2016). doi:10.1051/cocv/2015024 Google Scholar |
[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, 53-75 (2003) Google Scholar |
[21] |
Wonham, WM:On a matrix Riccati equation of stochastic control. SIAM J. Control Optim 6, 681-697(1968) Google Scholar |
[22] |
Yong, J:Linear-quadratic optimal control problems for mean-field stochastic differential equations. SIAM J. Control Optim 51, 2809-2838 (2013) Google Scholar |
[23] |
Yong, J, Zhou, XY:Stochastic controls:Hamiltonian systems and HJB equations. Springer-Verlag, New York (1999) Google Scholar |
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