-
Previous Article
Semicontinuity of approximate solution mappings to generalized vector equilibrium problems
- JIMO Home
- This Issue
-
Next Article
Stability analysis of a delayed social epidemics model with general contact rate and its optimal control
A necessary condition for mean-field type stochastic differential equations with correlated state and observation noises
1. | College of Sciences, Shandong Jiaotong University, Jinan 250023, China |
References:
[1] |
D. Andersson and B. Djehiche, A maximum principle for SDEs of mean-field type,, Appl. Math. Optim., 63 (2011), 341.
doi: 10.1007/s00245-010-9123-8. |
[2] |
A. Bensoussan, Stochastic Control of Partially Observable Systems,, Cambridge University Press, (1992).
doi: 10.1017/CBO9780511526503. |
[3] |
R. Buckdahn, J. Li and S. Peng, Mean-field backward stochastic differential equations and related partial differential equations,, Stochastic Process. Appl., 119 (2009), 3133.
doi: 10.1016/j.spa.2009.05.002. |
[4] |
X. Cui, X. Li and D. Li, Unified framework of mean-field formulations for optimal multi-period mean-variance portfolio selection,, IEEE Trans. Automat. Control, 59 (2014), 1833.
doi: 10.1109/TAC.2014.2311875. |
[5] |
R. Elliott, X. Li and Y. Ni, Discrete time mean-field stochastic linear quadratic optimal control problems,, Automatica, 49 (2013), 3222.
doi: 10.1016/j.automatica.2013.08.017. |
[6] |
M. Hafayed, A mean-field maximum principle for optimal control of forward-backward stochastic differential equations with Poisson jump processes,, Int. J. Dynam. Control, 1 (2013), 300.
doi: 10.1007/s40435-013-0027-8. |
[7] |
M. Hafayed, A mean-field necessary and sufficient conditions for optimal singular stochastic control,, Commun. Math. Stat., 1 (2013), 417.
doi: 10.1007/s40304-014-0023-0. |
[8] |
M. Hafayed, Singular mean-field optimal control for forward-backward stochastic systems and applications to finance,, Int. J. Dynam. Control, 2 (2014), 542.
doi: 10.1007/s40435-014-0080-y. |
[9] |
M. Hafayed, A. Abba and S. Abbas, On mean-field stochastic maximum principle for near optimal controls for poisson jump diffusion with applications,, Int. J. Dynam. Control, 2 (2014), 262.
doi: 10.1007/s40435-013-0040-y. |
[10] |
M. Hafayed and S. Abbas, On near-optimal mean-field stochastic singular controls: Necessary and sufficient conditions for near-optimality,, J. Optim. Theory Appl., 160 (2014), 778.
doi: 10.1007/s10957-013-0361-1. |
[11] |
J. Huang, X. Li and J. Yong, A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon,, Math. Control Relat. Fields, 5 (2015), 97.
doi: 10.3934/mcrf.2015.5.97. |
[12] |
J. Huang, G. Wang and Z. Wu, Optimal premium policy of an insurance firm: Full and partial information,, Insurance: Math. Econ., 47 (2010), 208.
doi: 10.1016/j.insmatheco.2010.04.007. |
[13] |
T. Meyer-Brandis, B. Øksendal and X. Zhou, A mean-field stochastic maximum principle via Malliavin calculus,, Stochastics, 84 (2012), 643.
doi: 10.1080/17442508.2011.651619. |
[14] |
Y. Ni, J. Zhang and X. Li, Indefinite mean-field stochastic linear-quadratic optimal control,, IEEE Trans. Automat. Control, 60 (2015), 1786.
doi: 10.1109/TAC.2014.2385253. |
[15] |
G. Wang and Z. Wu, Kalman-Bucy filtering equations of forward and backward stochastic systems and applications to recursive optimal control problems,, J. Math. Anal. Appl., 342 (2008), 1280.
doi: 10.1016/j.jmaa.2007.12.072. |
[16] |
G. Wang, Z. Wu and J. Xiong, Maximum principle for forward-backward stochastic control systems with corrected state and observation noises,, SIAM J. Control Optim., 51 (2013), 491.
doi: 10.1137/110846920. |
[17] |
G. Wang, Z. Wu and C. Zhang, Maximum principles for partially observed mean-field stochastic systems with applications to financial engineering,, Proceedings of the 33rd Chinese Control Conference, (2014), 28.
doi: 10.1109/ChiCC.2014.6895853. |
[18] |
G. Wang, C. Zhang and W. Zhang, Stochastic maximum principle for mean-field type optimal control under partial information,, IEEE Trans. Automat. Control, 59 (2014), 522.
doi: 10.1109/TAC.2013.2273265. |
[19] |
W. M. Wonham, On the separation theorem of stochastic control,, SIAM J. Control, 6 (1968), 312.
doi: 10.1137/0306023. |
[20] |
H. Xiao and G. Wang, The filtering equations of forward-backward stochastic systems with random jumps and applications to partial information stochastic optimal control,, Stoch. Anal. Appl., 28 (2010), 1003.
doi: 10.1080/07362994.2010.515480. |
[21] |
J. Xiong, An Introduction to Stochastic Filtering Theory,, Oxford University Press, (2008).
|
[22] |
J. Yong, Linear-quadratic optimal control problems for mean-field stochastic differential equations,, SIAM J. Control Optim., 51 (2013), 2809.
doi: 10.1137/120892477. |
show all references
References:
[1] |
D. Andersson and B. Djehiche, A maximum principle for SDEs of mean-field type,, Appl. Math. Optim., 63 (2011), 341.
doi: 10.1007/s00245-010-9123-8. |
[2] |
A. Bensoussan, Stochastic Control of Partially Observable Systems,, Cambridge University Press, (1992).
doi: 10.1017/CBO9780511526503. |
[3] |
R. Buckdahn, J. Li and S. Peng, Mean-field backward stochastic differential equations and related partial differential equations,, Stochastic Process. Appl., 119 (2009), 3133.
doi: 10.1016/j.spa.2009.05.002. |
[4] |
X. Cui, X. Li and D. Li, Unified framework of mean-field formulations for optimal multi-period mean-variance portfolio selection,, IEEE Trans. Automat. Control, 59 (2014), 1833.
doi: 10.1109/TAC.2014.2311875. |
[5] |
R. Elliott, X. Li and Y. Ni, Discrete time mean-field stochastic linear quadratic optimal control problems,, Automatica, 49 (2013), 3222.
doi: 10.1016/j.automatica.2013.08.017. |
[6] |
M. Hafayed, A mean-field maximum principle for optimal control of forward-backward stochastic differential equations with Poisson jump processes,, Int. J. Dynam. Control, 1 (2013), 300.
doi: 10.1007/s40435-013-0027-8. |
[7] |
M. Hafayed, A mean-field necessary and sufficient conditions for optimal singular stochastic control,, Commun. Math. Stat., 1 (2013), 417.
doi: 10.1007/s40304-014-0023-0. |
[8] |
M. Hafayed, Singular mean-field optimal control for forward-backward stochastic systems and applications to finance,, Int. J. Dynam. Control, 2 (2014), 542.
doi: 10.1007/s40435-014-0080-y. |
[9] |
M. Hafayed, A. Abba and S. Abbas, On mean-field stochastic maximum principle for near optimal controls for poisson jump diffusion with applications,, Int. J. Dynam. Control, 2 (2014), 262.
doi: 10.1007/s40435-013-0040-y. |
[10] |
M. Hafayed and S. Abbas, On near-optimal mean-field stochastic singular controls: Necessary and sufficient conditions for near-optimality,, J. Optim. Theory Appl., 160 (2014), 778.
doi: 10.1007/s10957-013-0361-1. |
[11] |
J. Huang, X. Li and J. Yong, A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon,, Math. Control Relat. Fields, 5 (2015), 97.
doi: 10.3934/mcrf.2015.5.97. |
[12] |
J. Huang, G. Wang and Z. Wu, Optimal premium policy of an insurance firm: Full and partial information,, Insurance: Math. Econ., 47 (2010), 208.
doi: 10.1016/j.insmatheco.2010.04.007. |
[13] |
T. Meyer-Brandis, B. Øksendal and X. Zhou, A mean-field stochastic maximum principle via Malliavin calculus,, Stochastics, 84 (2012), 643.
doi: 10.1080/17442508.2011.651619. |
[14] |
Y. Ni, J. Zhang and X. Li, Indefinite mean-field stochastic linear-quadratic optimal control,, IEEE Trans. Automat. Control, 60 (2015), 1786.
doi: 10.1109/TAC.2014.2385253. |
[15] |
G. Wang and Z. Wu, Kalman-Bucy filtering equations of forward and backward stochastic systems and applications to recursive optimal control problems,, J. Math. Anal. Appl., 342 (2008), 1280.
doi: 10.1016/j.jmaa.2007.12.072. |
[16] |
G. Wang, Z. Wu and J. Xiong, Maximum principle for forward-backward stochastic control systems with corrected state and observation noises,, SIAM J. Control Optim., 51 (2013), 491.
doi: 10.1137/110846920. |
[17] |
G. Wang, Z. Wu and C. Zhang, Maximum principles for partially observed mean-field stochastic systems with applications to financial engineering,, Proceedings of the 33rd Chinese Control Conference, (2014), 28.
doi: 10.1109/ChiCC.2014.6895853. |
[18] |
G. Wang, C. Zhang and W. Zhang, Stochastic maximum principle for mean-field type optimal control under partial information,, IEEE Trans. Automat. Control, 59 (2014), 522.
doi: 10.1109/TAC.2013.2273265. |
[19] |
W. M. Wonham, On the separation theorem of stochastic control,, SIAM J. Control, 6 (1968), 312.
doi: 10.1137/0306023. |
[20] |
H. Xiao and G. Wang, The filtering equations of forward-backward stochastic systems with random jumps and applications to partial information stochastic optimal control,, Stoch. Anal. Appl., 28 (2010), 1003.
doi: 10.1080/07362994.2010.515480. |
[21] |
J. Xiong, An Introduction to Stochastic Filtering Theory,, Oxford University Press, (2008).
|
[22] |
J. Yong, Linear-quadratic optimal control problems for mean-field stochastic differential equations,, SIAM J. Control Optim., 51 (2013), 2809.
doi: 10.1137/120892477. |
[1] |
Guirong Jiang, Qishao Lu. The dynamics of a Prey-Predator model with impulsive state feedback control. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1301-1320. doi: 10.3934/dcdsb.2006.6.1301 |
[2] |
Yves Dumont, Frederic Chiroleu. Vector control for the Chikungunya disease. Mathematical Biosciences & Engineering, 2010, 7 (2) : 313-345. doi: 10.3934/mbe.2010.7.313 |
[3] |
J. Frédéric Bonnans, Justina Gianatti, Francisco J. Silva. On the convergence of the Sakawa-Shindo algorithm in stochastic control. Mathematical Control & Related Fields, 2016, 6 (3) : 391-406. doi: 10.3934/mcrf.2016008 |
[4] |
Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, 2013, 2013 (special) : 437-446. doi: 10.3934/proc.2013.2013.437 |
[5] |
Alberto Bressan, Ke Han, Franco Rampazzo. On the control of non holonomic systems by active constraints. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3329-3353. doi: 10.3934/dcds.2013.33.3329 |
[6] |
Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183 |
[7] |
A. K. Misra, Anupama Sharma, Jia Li. A mathematical model for control of vector borne diseases through media campaigns. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1909-1927. doi: 10.3934/dcdsb.2013.18.1909 |
[8] |
Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399 |
[9] |
Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521 |
[10] |
Peter Benner, Jens Saak, M. Monir Uddin. Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 1-20. doi: 10.3934/naco.2016.6.1 |
[11] |
Michael Grinfeld, Amy Novick-Cohen. Some remarks on stability for a phase field model with memory. Discrete & Continuous Dynamical Systems - A, 2006, 15 (4) : 1089-1117. doi: 10.3934/dcds.2006.15.1089 |
[12] |
Y. Latushkin, B. Layton. The optimal gap condition for invariant manifolds. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 233-268. doi: 10.3934/dcds.1999.5.233 |
[13] |
Yunfei Lv, Rong Yuan, Yuan He. Wavefronts of a stage structured model with state--dependent delay. Discrete & Continuous Dynamical Systems - A, 2015, 35 (10) : 4931-4954. doi: 10.3934/dcds.2015.35.4931 |
[14] |
Daoyuan Fang, Ting Zhang. Compressible Navier-Stokes equations with vacuum state in one dimension. Communications on Pure & Applied Analysis, 2004, 3 (4) : 675-694. doi: 10.3934/cpaa.2004.3.675 |
[15] |
Guido De Philippis, Antonio De Rosa, Jonas Hirsch. The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals. Discrete & Continuous Dynamical Systems - A, 2019, 39 (12) : 7031-7056. doi: 10.3934/dcds.2019243 |
[16] |
Bin Pei, Yong Xu, Yuzhen Bai. Convergence of p-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1141-1158. doi: 10.3934/dcdsb.2019213 |
[17] |
Carlos Gutierrez, Nguyen Van Chau. A remark on an eigenvalue condition for the global injectivity of differentiable maps of $R^2$. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 397-402. doi: 10.3934/dcds.2007.17.397 |
[18] |
Mansour Shrahili, Ravi Shanker Dubey, Ahmed Shafay. Inclusion of fading memory to Banister model of changes in physical condition. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 881-888. doi: 10.3934/dcdss.2020051 |
[19] |
Yizhuo Wang, Shangjiang Guo. A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1627-1652. doi: 10.3934/dcdsb.2018223 |
[20] |
Tomáš Roubíček. An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 867-893. doi: 10.3934/dcdss.2017044 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]