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Partially observed optimal controls of forward-backward doubly stochastic systems∗

Published online by Cambridge University Press:  03 June 2013

Yufeng Shi and
Qingfeng Zhu
Yufeng Shi
Affiliation:
School of Mathematics, Shandong University, 250100 Jinan, P.R. China. yfshi@sdu.edu.cn
Qingfeng Zhu
Affiliation:
School of Mathematics, Shandong University, 250100 Jinan, P.R. China. yfshi@sdu.edu.cnSchool of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, 250014 Jinan, P.R. China

Abstract

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The partially observed optimal control problem is considered for forward-backward doubly stochastic systems with controls entering into the diffusion and the observation. The maximum principle is proven for the partially observable optimal control problems. A probabilistic approach is used, and the adjoint processes are characterized as solutions of related forward-backward doubly stochastic differential equations in finite-dimensional spaces. Then, our theoretical result is applied to study a partially-observed linear-quadratic optimal control problem for a fully coupled forward-backward doubly stochastic system.

Keywords

Forward-backward doubly stochastic systempartially observed optimal controlmaximum principleadjoint equation

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 3 , July 2013, pp. 828 - 843
Copyright
© EDP Sciences, SMAI, 2013

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