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The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not contain the control variable, but the control domain need not to be convex. We apply our stochastic maximum principle (SMP in short) to investigate the optimal control problems of a class of stochastic partial differential equations (SPDEs in short). And as an example of the SMP, we solve a kind of forward-backward doubly stochastic linear quadratic optimal control problems as well. In the last section, we use the solution of FBDSDEs to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and open-loop Nash equilibrium point for nonzero sum stochastic differential games problem.
@article{COCV_2011__17_4_1174_0,
author = {Zhang, Liangquan and Shi, Yufeng},
title = {Maximum principle for forward-backward doubly stochastic control systems and applications},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1174--1197},
publisher = {EDP-Sciences},
volume = {17},
number = {4},
year = {2011},
doi = {10.1051/cocv/2010042},
mrnumber = {2859871},
zbl = {1236.93155},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010042/}
}
TY - JOUR AU - Zhang, Liangquan AU - Shi, Yufeng TI - Maximum principle for forward-backward doubly stochastic control systems and applications JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 1174 EP - 1197 VL - 17 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010042/ DO - 10.1051/cocv/2010042 LA - en ID - COCV_2011__17_4_1174_0 ER -
%0 Journal Article %A Zhang, Liangquan %A Shi, Yufeng %T Maximum principle for forward-backward doubly stochastic control systems and applications %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 1174-1197 %V 17 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010042/ %R 10.1051/cocv/2010042 %G en %F COCV_2011__17_4_1174_0
Zhang, Liangquan; Shi, Yufeng. Maximum principle for forward-backward doubly stochastic control systems and applications. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 1174-1197. doi: 10.1051/cocv/2010042
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