Equivalent cost functionals and stochastic linear quadratic optimal control problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 78-90.

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.

DOI : 10.1051/cocv/2011206
Classification : 93E20, 49N10, 60H10
Mots-clés : stochastic LQ problem, stochastic hamiltonian system, forward-backward stochastic differential equation, Riccati equation, stochastic maximum principle 
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     title = {Equivalent cost functionals and stochastic linear quadratic optimal control problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {78--90},
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     volume = {19},
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     zbl = {1258.93129},
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     url = {http://www.numdam.org/articles/10.1051/cocv/2011206/}
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Yu, Zhiyong. Equivalent cost functionals and stochastic linear quadratic optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 78-90. doi : 10.1051/cocv/2011206. http://www.numdam.org/articles/10.1051/cocv/2011206/

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