Open Access
Issue |
ESAIM: COCV
Volume 28, 2022
|
|
---|---|---|
Article Number | 17 | |
Number of page(s) | 43 | |
DOI | https://doi.org/10.1051/cocv/2022010 | |
Published online | 24 February 2022 |
- B. Acciaio, J. Backhoff-Veraguas and R. Carmona, Extended mean field control problems: stochastic maximum principle and transport perspective. SIAM J. Control Optim. 57 (2019) 3666–3693. [Google Scholar]
- S. Ahuja, Wellposedness of mean field games with common noise under a weak monotonicity conditions. Arxiv:1406.7028 (2015). [Google Scholar]
- D. Andersson and B. Djehiche, A maximum principle for SDEs of mean-field type. Appl. Math. Optim. 63 (2011) 341–356. [Google Scholar]
- A. Bensoussan, Stochastic control of partially observable systems. Cambridge University Press, Cambridge (1992). [CrossRef] [Google Scholar]
- A. Bensoussan, X. Feng and J. Huang, Linear-quadratic-Gaussian mean-field-game with partial observation and common noise. Math. Control Related Fields 11 (2021) 23–46. [CrossRef] [MathSciNet] [Google Scholar]
- A. Bensoussan, J. Frehse and S. Yam, Mean field games and mean field type control theory. Springer, New York (2013). [CrossRef] [Google Scholar]
- A. Bensoussan, S. Yam and Z. Zhang, Well-posedness of mean field type forward-backward stochastic differential equations. Stochastic Process. Appl. 125 (2015) 3327–3354. [CrossRef] [MathSciNet] [Google Scholar]
- R. Buckdahn, B. Djehiche, J. Li and S. Peng, Mean-field backward stochastic differential equations: a limit approach. Ann. Probab. 37 (2009) 1524–1565. [Google Scholar]
- R. Buckdahn, Y. Chen and J. Li, Partial derivative with respect to the measure and its applications to general controlled mean-field systems. Stochatic Process. Appl., DOI: https://doi.org/10.1016/j.spa.2021.01.003 (2021). [Google Scholar]
- R. Buckdahn, B. Djehiche and J. Li, A general stochastic maximum principle for SDEs of mean-field type. Appl. Math. Optim. 64 (2011) 197–216. [Google Scholar]
- R. Buckdahn, J. Li and J. Ma, A stochastic maximum principle for general mean-field systems. Appl. Math. Optim. 74 (2016) 507–534. [Google Scholar]
- R. Buckdahn, J. Li and J. Ma, A mean-field stochastic control problem with partial observations. Ann. Appl. Probab. 27 (2017) 3201–3245. [CrossRef] [MathSciNet] [Google Scholar]
- R. Buckdahn, J. Li and S. Peng, Mean-field backward stochastic differential equations and related partial differential equations. Stochatic Process. Appl. 19 (2009) 3133–3154. [CrossRef] [Google Scholar]
- P. Caines and A. Kizikale, ϵ-Nash equilibria for partially observed LQG mean field games with a major player. IEEE Trans. Automat. Control 62 (2017) 3225–3234. [CrossRef] [MathSciNet] [Google Scholar]
- P. Cardaliaguet, Notes on the mean field games. Notes from P. L. Lions’ lecture at the Collège de France (2012). [Google Scholar]
- R. Carmona and F. Delarue, Forward-backward stochastic differential equations and controlled Mckean-Vlasov dynamics. Ann. Probab. 43 (2015) 2647–2700. [CrossRef] [MathSciNet] [Google Scholar]
- R. Carmona and F. Delarue, Probabilistic theory of mean-field games with applications. Springer (2018). [Google Scholar]
- P. Graber, Linear quadratic mean field type control and mean field games with common noise, with applications to production of exhaustible resource. Appl. Math. Optim. 74 (2016) 459–486. [CrossRef] [MathSciNet] [Google Scholar]
- M. Hafayed, S. Abbas and A. Abba, On mean-field partial information maximum principle of optimal control for stochastic systems with Lévy processes. J. Optim. Theory Appl. 167 (2015) 1051–1069. [CrossRef] [MathSciNet] [Google Scholar]
- M. Huang, R. Malhamé and P. Caines, Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6 (2006) 221–251. [Google Scholar]
- M. Huang, P. Caines and R. Malhamé, Distributed multi-agent decision-making with partial observations: Asymptotic Nash equilibria. Proceeding of the 17th International Symosium on Mathematical Theory of Networks and Systems, Kyoto University, Kyoto, Japan (2006) 2727–30. [Google Scholar]
- B. Jourdain, S. Méléard and W.A. Woyczynski, Nonlinear SDEs driven by Lévy processes and related PDEs. ALEA Lat. Am. J. Probab. Math. Stat. 4 (2008) 1–29. [MathSciNet] [Google Scholar]
- M. Kac, Foundations of kinetic theory. In Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability 3 (1956) 171–197. [Google Scholar]
- J. Lasry and P. Lions, Jeux à champ moyen.I. Le cas stationnaire. Compt. Rend. Math. 343 (2006) 619–625. [Google Scholar]
- J. Lasry and P. Lions, Jeux à champ moyen.II. Horizon fini et contrôle optimal. Comp. Rend. Math. 343 (2006) 679–684. [Google Scholar]
- J.M. Lasry and P.L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [CrossRef] [MathSciNet] [Google Scholar]
- J. Li, Stochastic maximum principle in mean-field controls. Automatica 48 (2012) 366–373. [CrossRef] [MathSciNet] [Google Scholar]
- R. Li and F. Fu, The maximum principle for for partially observed optimal control problems of mean-field FBSDEs. Int. J. Control 92 (2019) 2463–2472. [CrossRef] [Google Scholar]
- R. Li and B. Liu, A maximum principle for fully coupled stochastic control systems of mean-field type. J. Math. Anal. Appl. 415 (2014) 902–930. [CrossRef] [MathSciNet] [Google Scholar]
- X. Li, J. Sun and J. Xiong, Linear quadratic optimal control problems for mean-field backward stochastic differential equations. Appl. Math. Optim. 74 (2019) 459–486. [Google Scholar]
- H. Ma and B. Liu, Linear-quadratic optimal control problem for partially observed forward-backward stochastic differential equations of mean-field type. Asian J. Control 19 (2017) 1–12. [CrossRef] [MathSciNet] [Google Scholar]
- S. Meherrem and M. Hafayed, Maximum principle for optimal control of McKean-Vlasov FBSDEs with Lévy process via the differentiability with respect to probability law. Optim. Control Appl. Meth. 40 (2019) 499–516. [CrossRef] [Google Scholar]
- T. Meyer-Brandis, B. Øksendal and X. Zhou, A mean-field stochastic maximum principle via Malliavin calculus. Stochastics 84 (2012) 643–666. [CrossRef] [MathSciNet] [Google Scholar]
- J. Moon and T. Başar, Linear quadratic risk-sensitive and robust mean field games. IEEE Trans. Automat. Control 62 (2017) 1062–1077. [CrossRef] [MathSciNet] [Google Scholar]
- E. Pardoux and A. Rascanu. Stochastic differential equations, backward SDEs and partial differential equations. Springer, Switzerland (2014). [Google Scholar]
- S. Peng, Backward stochastic differential equations and applications to optimal control. Appl. Math. Optim. 28 (1993) 125–144. [CrossRef] [MathSciNet] [Google Scholar]
- H. Phamand X. Wei, Bellman equations and viscosity solutions for mean field stochastic control problem. ESAIM: COCV 24 (2018) 437–461. [CrossRef] [EDP Sciences] [Google Scholar]
- N. Şen and P. Caines, Mean field game theory with a partially observed major agent. SIAM J. Control Optim. 54 (2016) 3174–3224. [CrossRef] [MathSciNet] [Google Scholar]
- N. Şen and P. Caines, Mean field games with partial observation. SIAM J. Control Optim. 57 (2019) 2064–2091. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Shen, Q. Meng and P. Shi, Maximum principle for mean-field jump-diffusion stochastic delay differential equations and its application to finance. Automatica J. IFAC 50 (2014) 1565–1579. [CrossRef] [MathSciNet] [Google Scholar]
- S. Tang, The maximum principle for partially observed optimal control of stochastic differential equations. SIAM J. Control Optim. 36 (1998) 1596–1617. [CrossRef] [MathSciNet] [Google Scholar]
- H. Tembine, Q. Zhu and T. Basar, Risk-sensitive mean-field stochastic differential games. IEEE Trans. Automat. Control 59 (2014) 835–850. [CrossRef] [MathSciNet] [Google Scholar]
- G. Wang, H. Xiao and G. Xing, An optimal control problem for mean-field forward-backward stochastic differential equation with noisy observation. Automatica J. IFAC 86 (2017) 104–109. [CrossRef] [MathSciNet] [Google Scholar]
- G. Wangand Z. Wu, The maximum principles for stochastic recursive optimal control problems under partial information. IEEE Trans. Automat. Control 54 (2009) 1230–1242. [CrossRef] [MathSciNet] [Google Scholar]
- G. Wang, Z. Wu and J. Xiong, Maximum principles for forward-backward stochastic control systems with correlated state and observation noises. SIAM J. Control Optim. 51 (2013) 491–524. [CrossRef] [MathSciNet] [Google Scholar]
- G. Wang, Z. Wu and J. Xiong, An introduction to optimal control of FBSDE with incomplete information. Springer, Cham (2018). [CrossRef] [Google Scholar]
- 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) 522–528. [CrossRef] [MathSciNet] [Google Scholar]
- Z. Wu, A maximum principle for partially observed optimal control of forward-backward stochastic control systems, vol. 53. Springer-Verlag, Berlin (2010) 2205–2214. [Google Scholar]
- J. Xiong, An Introduction to Stochastic Filtering Theory. Oxford University Press, London (2008). [Google Scholar]
- J. Yong, Linear-quadratic optimal control problems for mean-field stochastic differential equations. SIAM J. Control Optim. 51 (2013) 2809–2838. [Google Scholar]
- J. Yong and X. Zhou, Stochastic controls: Hamiltonian systems and HJB equations. Springer-Verlag, New York (1999). [Google Scholar]
- J. Zhang, Backward stochastic differential equations. From linear to fully nonlinear theory. Springer, New York (2017). [CrossRef] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.