Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T12:56:53.103Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic maximum principle for optimal control problem of forward and backward system

Published online by Cambridge University Press:  17 February 2009

Wensheng Xu
Wensheng Xu
Affiliation:
Department of Mathematics, Zhejiang University, Hongzhou 310027, China
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The maximum principle for optimal control problems of stochastic systems consisting of forward and backward state variables is proved, under the assumption that the diffusion coefficient does not contain the control variable, but the control domain need not be convex.

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 2 , October 1995 , pp. 172 - 185
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Ahmed, N. U., “Existence of optimal controls for a class of systems governed by differential inclusions on a Banach space”, J. Optim. Theory Appl. 50 (1986) 213–237.CrossRefGoogle Scholar
[2]Ahmed, N. U., “Relaxed controls for stochastic boundary value problems in finite dimension”, in Lecture notes in control and information science 149, (Springer, Berlin, 1991).Google Scholar
[3]Arkin, V. and Saksonov, M., “Necessary optimality conditions for stochastic differential equations”, Soviet Math. Dokl. 20 (1973) 1–5.Google Scholar
[4]Arkin, V. and Saksonov, M., “On the theory of the stochastic maximum principle in continuous time problems”, in Models and methods of stochastic optimization, (Central Economics and Mathematical Institute-Academy of Sciences of the USSR, 1983) 3–26.Google Scholar
[5]Bensoussam, A., “Lectures on stochastic control”, in Lecture notes in mathematics, 972, (Springer- Verlag, Berlin).Google Scholar
[6]Bismut, J. M., “Conjugate convex functions in optimal stochastic control”, J. Math. Anal. Appl. 44 (1973) 384–404.CrossRefGoogle Scholar
[7]Cadenillas, A. and Karatzas, I., “The stochastic maximum principle for linear convex optimal control with random coefficients”, SIAM J. Control Optim. (to appear).Google Scholar
[8]Elliott, R. J., “The optimal control of diffusions”, Appl. Math. Optim. 22 (1990) 229–240.CrossRefGoogle Scholar
[9]Ikeda, N. and Watanabe, S., Stochastic differential equations and diffusion processes (North Holland Publishing Company, 1981).Google Scholar
[10]Kushner, H. J., “Necessary conditions for continuous parameter stochastic optimization problems”, SIAM J. Control 10 (1972) 550–565.CrossRefGoogle Scholar
[11]Pardoux, E. and Peng, S., “Adapted solution of backward stochastic equation”, Systems and Control Letters 14 (1990) 55–61.CrossRefGoogle Scholar
[12]Peng, S., “A general stochastic maximum principle for optimal control problems“, SIAM J. Cont. 28 (1990) 966–979.Google Scholar
[13]Peng, S., “Backward stochastic differential equation and application to optimal control“, Appl. Math. Optim. 27 (1993) 125–144.CrossRefGoogle Scholar