A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information

Science in China, Series A: Mathematics

Volumn 52, Issue 7, 2009, Pages 1579-1588

  Meng, QingXin ^a,b  

^a HUZHOU UNIVERSITY   (China)

^b FUDAN UNIVERSITY   (China)

Author keywords

Maximum principle; Partial information; Stochastic optimal control

Indexed keywords

EID: 71249093378     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11425-009-0114-7     Document Type: Article

References (18)

1. Yong J M, Zhou X Y. Stochastic Controls, Hamilton Systems and HJB Equations. Appl Math, 43. New York: Springer-Verlag, 1999.
2. Oksendal B. A universal optimal consumption rate for insider. Math Finance, 16: 119-129 (2006).
3. Kohlmann M, Xiong D W. The mean-variance hedging of a default option with partial information. Stoch Anal Appl, 25: 869-893 (2007).
4. Bensoussan A. Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions. Stochastics, 9: 169-222 (1983).
5. Elliott R J, Kohlmann M. The variational principle for optimal control of diffusions with partial information. Systems Control Lett, 12: 63-89 (1989).
6. Kohlmann M. Optimality conditions in optimal control of jump processes-extended abstract. In: Proceedings in Operation Research, 7 (Sixth Annual Meeting, Deutsch. Gesellsch. Operation Res., Christian-Albrechts-Univ., Kiel, 1977). Berlin: Springer, 1997, 48-57.
7. Tang S J. The maximum principle for partially observed optimal control of stochastic differential equations. SIAM J Control Optim, 36: 1596-1617 (1998).
8. Baghery F, Oksendal B. A maximum principle for stochastic control with partial information. Stoch Anal Appl, 25: 493-514 (2007).
9. Antonelli F. Backward-forward stochastic differential equations. Ann Appl Probab, 3: 777-793 (1993).
10. Duffie D, Epstein L. Asset pricing with stochastic differential utilities. Rev Financial Stud, 5: 411-436 (1992).
11. El Karoui N, Peng S G, Quenez M C. Backward stochastic differential equations in finance. Math Finance, 7: 1-71 (1997).
12. Shi J T, Wu Z. The maximum principle for fully coupled forward backward stochastic control system. Acta Automat Sinica, 32: 161-169 (2006).
13. Wu Z. Maximum principle for optimal control problem of fully coupled forward-backward stochastic systems. Systems Sci Math Sci, 11: 249-259 (1998).
14. Xu W S. Stochastic maximum principle for optimal control problem of forward and backward system. J Aust Math Soc, 37: 172-185 (1995).
15. Hu Y, Peng S G. Solution of forward-backward stochastic differential equations. Probab Theory Related Fields, 103: 273-283 (1995).
16. Ma J, Protter P, Yong J M. Solving forward-backward stochastic differential equations explicitly-a four step scheme. Probab Theory Related Fields, 98: 339-359 (1994).
17. Ma J, Yong J M. Forward-backward stochastic differential equations and their applications. In: Lecture Notes Math, 1702. Berlin: Springer-Verlag, 1999.
18. Peng S G, Wu Z. Fully coupled forward-backward stochastic differential equations and applications to optimal control. SIAM J Control Optim, 37: 825-843 (1999).