Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 964765, 10 pages
http://dx.doi.org/10.1155/2013/964765
Research Article

Maximum Principle for Delayed Stochastic Linear-Quadratic Control Problem with State Constraint

School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China

Received 23 May 2013; Accepted 28 November 2013

Academic Editor: Donal O'Regan

Copyright © 2013 Feng Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Arriojas, Y. Hu, S.-E. Mohammed, and G. Pap, “A delayed Black and Scholes formula,” Stochastic Analysis and Applications, vol. 25, no. 2, pp. 471–492, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S.-E. Mohammed, Stochastic Functional Differential Equations, Pitman, 1984.
  3. S.-E. Mohammed, “Stochastic differential systems with memory: theory, examples and applications,” in Stochastic Analysis and Related Topics VI: Proceedings of the 6th Oslo—Silivri Workshop Geilo, Progress in Probability, Birkhäuser, Boston, Mass, USA, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J.-P. Richard, “Time-delay systems: an overview of some recent advances and open problems,” Automatica, vol. 39, no. 10, pp. 1667–1694, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. B. Øksenda and A. Sulem, “A maximum principle for optimal control of stochastic systems with delay, with applications to finance,” in Optimal Control and Partial Differential Equations, J. M. Menaldi, E. Rofman, and A. Sulem, Eds., pp. 64–79, ISO Press, Amsterdam, The Netherlands, 2000. View at Google Scholar
  6. S. Peng, “A general stochastic maximum principle for optimal control problems,” SIAM Journal on Control and Optimization, vol. 28, no. 4, pp. 966–979, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. Peng, “Backward stochastic differential equations and applications to optimal control,” Applied Mathematics and Optimization, vol. 27, no. 2, pp. 125–144, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Z. Wu, “Maximum principle for optimal control problem of fully coupled forward-backward stochastic systems,” Systems Science and Mathematical Sciences, vol. 11, no. 3, pp. 249–259, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Z. Wu, “A general maximum principle for optimal control of forward-backward stochastic systems,” Automatica, vol. 49, no. 5, pp. 1473–1480, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  10. W. Xu, “Stochastic maximum principle for optimal control problem of forward and backward system,” Australian Mathematical Society B, vol. 37, no. 2, pp. 172–185, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Yong, “Optimality variational principle for controlled forward-backward stochastic differential equations with mixed initial-terminal conditions,” SIAM Journal on Control and Optimization, vol. 48, no. 6, pp. 4119–4156, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Peng and Z. Yang, “Anticipated backward stochastic differential equations,” The Annals of Probability, vol. 37, no. 3, pp. 877–902, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. L. Chen and Z. Wu, “Maximum principle for the stochastic optimal control problem with delay and application,” Automatica, vol. 46, no. 6, pp. 1074–1080, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. Huang and J. Shi, “Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations,” ESAIM. Control, Optimisation and Calculus of Variations, vol. 18, no. 4, pp. 1073–1096, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Z. Yu, “The stochastic maximum principle for optimal control problems of delay systems involving continuous and impulse controls,” Automatica, vol. 48, no. 10, pp. 2420–2432, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. Tang and X. Li, “Necessary conditions for optimal control of stochastic systems with random jumps,” SIAM Journal on Control and Optimization, vol. 32, no. 5, pp. 1447–1475, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J. Yong and X. Y. Zhou, Stochastic Controls: Hamiltionian Systems and HJB Equations, Springer, New York, NY, USA, 1999. View at MathSciNet
  18. L. Chen, Z. Wu, and Z. Yu, “Delayed stochastic linear-quadratic control problem and related applications,” Journal of Applied Mathematics, vol. 2012, Article ID 835319, 22 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. J. Huang, X. Li, and J. Shi, “Forward-backward linear quadratic stochastic optimal control problem with delay,” Systems & Control Letters, vol. 61, no. 5, pp. 623–630, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet