Free Access
Issue
ESAIM: COCV
Volume 26, 2020
Article Number 41
Number of page(s) 34
DOI https://doi.org/10.1051/cocv/2019057
Published online 30 June 2020
  1. D. Andersson and B. Djehiche, A maximum principle for SDEs of mean-field type. Appl. Math. Optim. 63 (2011) 341–356. [Google Scholar]
  2. J.M. Bismut, Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. 14 (1976) 419–444. [Google Scholar]
  3. T. Björk, M. Khapko and A. Murgoci, On time-inconsistent stochastic control in continuous time. Finance Stoch. 21 (2017) 331–360. [CrossRef] [Google Scholar]
  4. 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]
  5. R. Buckdahn, B. Djehiche and J. Li, A general maximum principle for SDEs of mean-field type. Appl. Math. Optim. 64 (2011) 197–216. [Google Scholar]
  6. R. Buckdahn, J. Li, S. Peng and C. Rainer, Mean-field stochastic differential equations and associated PDEs. Ann. Probab. 45 (2017) 824–878. [Google Scholar]
  7. R. Carmona, F. Delarue and A. Lachapelle, Control of McKean-Vlasov versus mean field games. Math. Fin. Econ. 7 (2013) 131–166. [CrossRef] [Google Scholar]
  8. S. Chen, X. Li and X. Zhou, Stochastic linear quadratic regulators with indefinite control weight costs. SIAM J. Control Optim. 36 (1998) 1685–1702. [Google Scholar]
  9. D. Dawson, Critical dynamics and fluctuations for a mean-field model of cooperative behavior. J. Statist. Phys. 31 (1983) 29–85. [CrossRef] [MathSciNet] [Google Scholar]
  10. Y. Hu, H. Jin and X. Zhou, Time-inconsistent stochastic linear-quadratic control. SIAM J. Control Optim. 50 (2012) 1548–1572. [Google Scholar]
  11. Y. Hu, H. Jin and X. Zhou, Time-inconsistent stochastic linear-quadratic control: characterization and uniqueness of equilibrium. SIAM J. Control Optim. 55 (2017) 1261–1279. [Google Scholar]
  12. M. Huang, R. Malhame and P. Caines, Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6 (2006) 221–252. [Google Scholar]
  13. M. Kac, Foundations of kinetic theory, in Proceedings of the 3rd Berkeley symposium on mathematical statistics and probability, Vol. 3 University of California Press, California (1956) 171–197. [Google Scholar]
  14. X. Li, J. Sun and J. Yong, Mean-field stochastic linear quadratic optimal control problems: closed-loop solvability. Prob. Uncer. Quan Risk 1 (2016) 2. [CrossRef] [Google Scholar]
  15. H. McKean, A class of Markov processes associated with nonlinear parabolic equations. Proc. Natl. Acad. Sci. USA 56 (1966) 1907–1911. [CrossRef] [Google Scholar]
  16. T. Meyer-Brandis, B. Øksendal and X. Zhou, A mean-field stochastic maximum principle via Malliavin calculus. Stochastics 84 (2012) 643–666. [CrossRef] [Google Scholar]
  17. S. Tang, General linear quadratic optimal stochastic control problems with random coefficients: linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM J. Control Optim. 42 (2003) 53–75. [Google Scholar]
  18. T. Wang, Equilibrium controls in time inconsistent stochastic linear quadratic problems. Appl. Math. Optim. 81 (2020) 591–619. [Google Scholar]
  19. T. Wang, Characterizations of equilibrium controls in time inconsistent mean-field stochastic linear quadratic problems. I. Math. Control Relat. Field 9 (2019) 385–409. [CrossRef] [Google Scholar]
  20. W. Wonham, On a matrix Riccati equation of stochastic control. SIAM J. Control 6 (1968) 681–697. [CrossRef] [Google Scholar]
  21. Q. Wei, J. Yong and Z. Yu, Time-inconsistent recursive stochastic optimal control problems. SIAM J. Control Optim. 55 (2017) 4156–4201. [Google Scholar]
  22. J. Yong, Time-inconsistent optimal control problem and the equilibrium HJB equation. Math. Control Related Fields 2 (2012) 271–329. [CrossRef] [Google Scholar]
  23. J. Yong, A linear-quadratic optimal control problem for mean-field stochastic differential equations. SIAM J. Control Optim. 51 (2013) 2809–2838. [Google Scholar]
  24. J. Yong, Linear-quadratic optimal control problems for mean-field stochastic differential equations – time-consistent solutions. Trans. Amer. Math. Soc. 369 (2017) 5467–5523. [CrossRef] [Google Scholar]
  25. J. Yong and X. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer-Verlag, New York (1999). [Google Scholar]

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