Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-07T23:25:20.338Z Has data issue: false hasContentIssue false
  • English
  • Français

General necessary conditions for partially observed optimal stochastic controls

Part of: Stochastic systems and control Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Xunjing Li  and
Shanjian Tang
Xunjing Li*
Affiliation:
Fudan University
Shanjian Tang*
Affiliation:
Fudan University
*
∗Postal address: Department of Mathematics, Fudan University, Shanghai 200433, People's Republic of China.
∗Postal address: Department of Mathematics, Fudan University, Shanghai 200433, People's Republic of China.
Get access Rights & Permissions [Opens in a new window]

Abstract

The partially observed control problem is considered for stochastic processes with control entering into the diffusion and the observation. The maximum principle is proved for the partially observable optimal control. A pure probabilistic approach is used, and the adjoint processes are characterized as solutions of related backward stochastic differential equations in finite-dimensional spaces. Most of the derivation is identified with that of the completely observable case.

Keywords

MAXIMUM PRINCIPLEPARTIAL OBSERVATIONFIRST AND SECOND ADJOINT PROCESSES

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 60G35: Signal detection and filtering
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 1118 - 1137
Copyright
Copyright © Applied Probability Trust 1995 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research partially supported by the NSF of China and the Chinese State Education Commission Science Foundation.

References

[1] Baras, J. S., Elliott, R. J. and Kohlmann, M. (1989) The partially observed stochastic minimum principle. SIAM J. Control Optim. 27, 1279–1292.Google Scholar
[2] Bensoussan, A. (1983) Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions. Stochastics 9, 169–222.Google Scholar
[3] Fleming, W. H. (1968) Optimal control of partially observable diffusions. SIAM J. Control 6, 194–214.CrossRefGoogle Scholar
[4] Haussmann, U. G. (1987) The maximum principle for optimal control of diffusions with partial information. SIAM J. Control Optim. 25, 341–361.CrossRefGoogle Scholar
[5] Peng, S. G. (1990) A general stochastic maximum principle for optimal control problems. SIAM J. Control Optim. 28, 966–979.Google Scholar
[6] Tang, S. J. and Li, X. J. (1994) Necessary conditions for optimal control of stochastic systems with random jumps. SIAM J. Control Optim. 32, 1447–1475.Google Scholar
[7] Zhou, X. Y. (1993) On the necessary conditions of optimal controls for stochastic partial differential equations. SIAM J. Control Optim. 31, 1462–1478.Google Scholar