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Equivalent cost functionals and stochastic linear quadraticoptimal control problems∗

Published online by Cambridge University Press:  23 February 2012

Zhiyong Yu
Zhiyong Yu*
Affiliation:
School of Economics, Shandong University, Jinan 250100, P.R. China. yuzhiyong@sdu.edu.cn

Abstract

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This paper is concerned with the stochastic linear quadratic optimal control problems (LQproblems, for short) for which the coefficients are allowed to be random and the costfunctionals are allowed to have negative weights on the square of control variables. Wepropose a new method, the equivalent cost functional method, to deal with the LQ problems.Comparing to the classical methods, the new method is simple, flexible and non-abstract.The new method can also be applied to deal with nonlinear optimization problems.

Keywords

Stochastic LQ problemstochastic Hamiltonian systemForward-backward stochastic differential equationRiccati equationstochastic maximum principle

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 1 , January 2013 , pp. 78 - 90
Copyright
© EDP Sciences, SMAI, 2012

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