# Maximum principle for forward-backward doubly stochastic control systems and applications*

ESAIM: Control, Optimisation and Calculus of Variations (2011)

- Volume: 17, Issue: 4, page 1174-1197
- ISSN: 1292-8119

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topZhang, Liangquan, and Shi, Yufeng. "Maximum principle for forward-backward doubly stochastic control systems and applications*." ESAIM: Control, Optimisation and Calculus of Variations 17.4 (2011): 1174-1197. <http://eudml.org/doc/221892>.

@article{Zhang2011,

abstract = {
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.
},

author = {Zhang, Liangquan, Shi, Yufeng},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Maximum principle; stochastic optimal control;
forward-backward doubly stochastic differential equations; spike variations;
variational equations; stochastic partial differential equations; nonzero
sum stochastic differential game; maximum principle; optimal control problems; fully coupled forward-backward doubly stochastic differential equations (FBDSDEs); stochastic maximum principle (SMP); stochastic partial differential equations (SPDEs)},

language = {eng},

month = {11},

number = {4},

pages = {1174-1197},

publisher = {EDP Sciences},

title = {Maximum principle for forward-backward doubly stochastic control systems and applications*},

url = {http://eudml.org/doc/221892},

volume = {17},

year = {2011},

}

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

DA - 2011/11//

PB - EDP Sciences

VL - 17

IS - 4

SP - 1174

EP - 1197

AB -
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.

LA - eng

KW - Maximum principle; stochastic optimal control;
forward-backward doubly stochastic differential equations; spike variations;
variational equations; stochastic partial differential equations; nonzero
sum stochastic differential game; maximum principle; optimal control problems; fully coupled forward-backward doubly stochastic differential equations (FBDSDEs); stochastic maximum principle (SMP); stochastic partial differential equations (SPDEs)

UR - http://eudml.org/doc/221892

ER -

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