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Dynamic programming principle for stochastic recursive optimalcontrol problem with delayed systems∗

Published online by Cambridge University Press:  16 January 2012

Li Chen  and
Zhen Wu
Li Chen
Affiliation:
Department of Mathematics, China University of Mining Technology, Beijing 100083, P.R. China. chenli@cumtb.edu.cn
Zhen Wu
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, P.R. China; wuzhen@sdu.edu.cn

Abstract

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In this paper, we study one kind of stochastic recursive optimal control problem for thesystems described by stochastic differential equations with delay (SDDE). In ourframework, not only the dynamics of the systems but also the recursive utility depend onthe past path segment of the state process in a general form. We give the dynamicprogramming principle for this kind of optimal control problems and show that the valuefunction is the viscosity solution of the corresponding infinite dimensionalHamilton-Jacobi-Bellman partial differential equation.

Keywords

Stochastic differential equation with delayrecursive optimal control problemdynamic programming principleHamilton-Jacobi-Bellman equation

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 4 , October 2012 , pp. 1005 - 1026
Copyright
© EDP Sciences, SMAI, 2012

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