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Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations∗

Published online by Cambridge University Press:  16 January 2012

Jianhui Huang  and
Jingtao Shi
Jianhui Huang
Affiliation:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, P.R. China. majhuang@inet.polyu.edu.hk
Jingtao Shi
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, P.R. China; shijingtao@sdu.edu.cn
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Abstract

This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient does not contain the control variables and the control domain is not necessarily convex. Both the necessary and sufficient conditions of optimality are proved. As illustrating examples, two kinds of linear quadratic control problems are discussed and both optimal controls are derived explicitly.

Keywords

Stochastic optimal controlmaximum principlestochastic differential delayed equationanticipated backward differential equationfully coupled forward-backward stochastic systemClarke generalized gradient
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 4 , October 2012 , pp. 1073 - 1096
Copyright
© EDP Sciences, SMAI, 2012

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