Open Access
Issue
ESAIM: COCV
Volume 27, 2021
Article Number 69
Number of page(s) 35
DOI https://doi.org/10.1051/cocv/2021066
Published online 02 July 2021
  1. J.-M. Bismut, Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. 14 (1976) 419–444. [CrossRef] [Google Scholar]
  2. 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]
  3. S. Chen and J. Yong, Stochastic linear quadratic optimal control problems. Appl. Math. Optim. 43 (2001) 21–45. [Google Scholar]
  4. Y. Hu and B. Oksendal, Partial information linear quadratic control for jump diffusions. SIAM J. Control Optim. 47 (2008) 1744–1761. [Google Scholar]
  5. J. Huang and Z. Yu, Solvability of indefinite stochastic Riccati equations and linear quadratic optimal control problems. Syst. Control Lett. 68 (2014) 68–75. [Google Scholar]
  6. Y. Ji and H. Chizeck, Jump linear quadratic Gaussian control in continuous time. IEEE Trans. Autom. Control. 37 (1992) 1884–1892. [Google Scholar]
  7. Y. Ji and H. Chizeck, Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control. IEEE Trans. Autom. Control. 35 (1990) 777–788. [Google Scholar]
  8. M. Kohlmann and S. Tang, New developments in backward stochastic riccati equations and their applications, in Mathematical Finance, edited by M. Kohlmann, S. Tang. Birkhäuser, Basel (2001) 194–214. [Google Scholar]
  9. M. Kohlmann and S. Tang, Global adapted solution of one-dimensional backward stochastic riccati equations, with application to the mean–variance hedging. Stoch. Process. Appl. 97 (2002) 255–288. [Google Scholar]
  10. M. Kohlmann and S. Tang, Minimization of risk and linear quadratic optimal control theory. SIAM J. Control Optim. 42 (2003) 1118–1142. [Google Scholar]
  11. M. Kohlmann and S. Tang, Multidimensional backward stochastic Riccati equations and applications. SIAM J. Control Optim. 41 (2003) 1696–1721. [Google Scholar]
  12. H. Kushner, Optimal stochastic control. IRE Trans. Autom. Control. 7 (1962) 120–122. [Google Scholar]
  13. N. Li, Z. Wu and Z. Yu, Indefinite stochastic linear-quadratic optimal control problems with random jumps and related stochastic Riccati equations. Sci. China Math. 61 (2018) 563–576. [Google Scholar]
  14. X. Li and X. Zhou, Indefinite stochastic LQ controls with Markovian jumps in a finite time horizon. Commun. Inf. Syst. 2 (2002) 265–282. [Google Scholar]
  15. X. Li, X. Zhou and M. Rami, Indefinite stochastic LQ control with jumps, in Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228). IEEE (2001). [Google Scholar]
  16. X. Li, X. Zhou and M.A. Rami, Indefinite stochastic linear quadratic control with Markovian jumps in infinite time horizon. J. Global Optim. 27 (2003) 149–175. [Google Scholar]
  17. Y. Liu, G. Yin and X.Y. Zhou, Near-optimal controls of random-switching LQ problems with indefinite control weight costs. Automatica. 41 (2005) 1063–1070. [Google Scholar]
  18. Q. Lv, T. Wang and X. Zhang, Characterization of optimal feedback for stochastic linear quadratic control problems. Probab. Uncert. Quant. Risk. 2 (2017) Article number: 11. [Google Scholar]
  19. H. Mei and J. Yong, Equilibrium strategies for time-inconsistent stochastic switching systems. ESAIM: COCV 25 (2019) Article number: 64. [Google Scholar]
  20. J. Sun, X. Li and J. Yong, Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems. SIAM J. Control Optim. 54 (2016) 2274–2308. [CrossRef] [MathSciNet] [Google Scholar]
  21. J. Sun, J. Xiong and J. Yong, Stochastic linear-quadratic optimal control problems with random coefficients: closed-loop representation of open-loop optimal controls. Manuscript submitted for publication. (2018). [Google Scholar]
  22. J. Sun and J. Yong, Linear quadratic stochastic differential games: open-loop and closed-loop saddle points. SIAM J. Control Optim. 52 (2014) 4082–4121. [Google Scholar]
  23. J. Sun and J. Yong, Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions. Springer International Publishing (2020). [CrossRef] [Google Scholar]
  24. 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. [CrossRef] [MathSciNet] [Google Scholar]
  25. S. Tang, Dynamic programming for general linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. 53 (2015) 1082–1106. [CrossRef] [Google Scholar]
  26. T. Wang, Necessary conditions in stochastic linear quadratic problems and their applications. J. Math. Anal. Appl. 469 (2019) 280–297. [Google Scholar]
  27. W.M. Wonham, On a matrix riccati equation of stochastic control. SIAM J. Control 6 (1968) 681–697. [CrossRef] [Google Scholar]
  28. Z. Wu and X.-R. Wang, FBSDE with Poisson process and its application to linear quadratic stochastic optimal control problem with random jumps. Acta Autom. Sin. 29 (2003) 821–826. [Google Scholar]
  29. G. Yin, X. Zhou, Markowitz’s mean-variance portfolio selection with Regime switching: from discrete-time models to their continuous-time limits. IEEE Trans. Autom. Control. 49 (2004) 349–360. [CrossRef] [Google Scholar]
  30. J. Yong and X. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer, New York (1999). [Google Scholar]
  31. Z. Yu, Infinite horizon jump-diffusion forward-backward stochastic differential equations and their application to backward linear-quadratic problems. ESAIM: COCV 23 (2017) 1331–1359. [CrossRef] [EDP Sciences] [Google Scholar]
  32. C. Zalinescu, On uniformly convex functions. J. Math. Anal. Appl. 95 (1983) 344–374. [Google Scholar]
  33. C. Zalinescu, Convex Analysis in General Vector Spaces. World Scientific (2002). [CrossRef] [Google Scholar]
  34. Q. Zhang and G. Yin, On nearly optimal controls of hybrid LQG problems. IEEE Trans. Autom. Control. 44 (1999) 2271–2282. [Google Scholar]
  35. X. Zhang, R.J. Elliott and T.K. Siu, A stochastic maximum principle for a Markov regime-switching jump-diffusion model and its application to finance. SIAM J. Control Optim. 50 (2012) 964–990. [Google Scholar]
  36. X. Zhang, R.J. Elliott, T.K. Siu and J. Guo, Markovian regime-switching market completion using additional Markov jump assets. IMA J. Manag. Math. 23 (2011) 283–305. [Google Scholar]
  37. X. Zhang, T.K. Siu and Q. Meng, Portfolio selection in the enlarged Markovian regime-switching market. SIAM J. Control Optim. 48 (2010) 3368–3388. [Google Scholar]
  38. X. Zhang, Z. Sun and J. Xiong, A general stochastic maximum principle for a Markov regime switching jump-diffusion model of mean-field type. SIAM J. Control Optim. 56 (2018) 2563–2592. [Google Scholar]
  39. X. Zhou and G. Yin, Markowitz’s mean-variance portfolio selection with regime switching: a continuous-time model. SIAM J. Control Optim. 42 (2003) 1466–1482. [Google Scholar]

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