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Dynamic programming principle for stochastic recursive optimal control 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
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Abstract

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

Keywords

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