This paper is concerned with the stochastic linear quadratic optimal control problems (LQ problems, for short) for which the coefficients are allowed to be random and the cost functionals are allowed to have negative weights on the square of control variables. We propose 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 problem, stochastic hamiltonian system, forward-backward stochastic differential equation, Riccati equation, stochastic maximum principle

@article{COCV_2013__19_1_78_0, author = {Yu, Zhiyong}, title = {Equivalent cost functionals and stochastic linear quadratic optimal control problems}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {78--90}, publisher = {EDP-Sciences}, volume = {19}, number = {1}, year = {2013}, doi = {10.1051/cocv/2011206}, mrnumber = {3023061}, zbl = {1258.93129}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2011206/} }

TY - JOUR AU - Yu, Zhiyong TI - Equivalent cost functionals and stochastic linear quadratic optimal control problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 78 EP - 90 VL - 19 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2011206/ DO - 10.1051/cocv/2011206 LA - en ID - COCV_2013__19_1_78_0 ER -

%0 Journal Article %A Yu, Zhiyong %T Equivalent cost functionals and stochastic linear quadratic optimal control problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 78-90 %V 19 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2011206/ %R 10.1051/cocv/2011206 %G en %F COCV_2013__19_1_78_0

Yu, Zhiyong. Equivalent cost functionals and stochastic linear quadratic optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 1, pp. 78-90. doi : 10.1051/cocv/2011206. http://archive.numdam.org/articles/10.1051/cocv/2011206/

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