Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations
ESAIM: Control, Optimisation and Calculus of Variations (2012)
- Volume: 18, Issue: 4, page 1073-1096
- ISSN: 1292-8119
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topHuang, Jianhui, and Shi, Jingtao. "Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations." ESAIM: Control, Optimisation and Calculus of Variations 18.4 (2012): 1073-1096. <http://eudml.org/doc/272939>.
@article{Huang2012,
abstract = {This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient does not contain the control variables and the control domain is not necessarily convex. Both the necessary and sufficient conditions of optimality are proved. As illustrating examples, two kinds of linear quadratic control problems are discussed and both optimal controls are derived explicitly.},
author = {Huang, Jianhui, Shi, Jingtao},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {stochastic optimal control; maximum principle; stochastic differential delayed equation; anticipated backward differential equation; fully coupled forward-backward stochastic system; Clarke generalized gradient; Clarke's generalized gradient},
language = {eng},
number = {4},
pages = {1073-1096},
publisher = {EDP-Sciences},
title = {Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations},
url = {http://eudml.org/doc/272939},
volume = {18},
year = {2012},
}
TY - JOUR
AU - Huang, Jianhui
AU - Shi, Jingtao
TI - Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2012
PB - EDP-Sciences
VL - 18
IS - 4
SP - 1073
EP - 1096
AB - This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient does not contain the control variables and the control domain is not necessarily convex. Both the necessary and sufficient conditions of optimality are proved. As illustrating examples, two kinds of linear quadratic control problems are discussed and both optimal controls are derived explicitly.
LA - eng
KW - stochastic optimal control; maximum principle; stochastic differential delayed equation; anticipated backward differential equation; fully coupled forward-backward stochastic system; Clarke generalized gradient; Clarke's generalized gradient
UR - http://eudml.org/doc/272939
ER -
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