Geodesic
Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1073-1096

Voir la notice de l'article provenant de la source Numdam

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.

DOI : 10.1051/cocv/2011204
Classification : 93E20, 60H10, 34K50
Keywords: stochastic optimal control, maximum principle, stochastic differential delayed equation, anticipated backward differential equation, fully coupled forward-backward stochastic system, Clarke generalized gradient 
@article{COCV_2012__18_4_1073_0,
     author = {Huang, Jianhui and Shi, Jingtao},
     title = {Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1073--1096},
     publisher = {EDP-Sciences},
     volume = {18},
     number = {4},
     year = {2012},
     doi = {10.1051/cocv/2011204},
     mrnumber = {3019473},
     zbl = {1258.93122},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011204/}
}
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
SP  - 1073
EP  - 1096
VL  - 18
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011204/
DO  - 10.1051/cocv/2011204
LA  - en
ID  - COCV_2012__18_4_1073_0
ER  - 
%0 Journal Article
%A Huang, Jianhui
%A Shi, Jingtao
%T Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2012
%P 1073-1096
%V 18
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011204/
%R 10.1051/cocv/2011204
%G en
%F COCV_2012__18_4_1073_0
Huang, Jianhui; Shi, Jingtao. Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1073-1096. doi: 10.1051/cocv/2011204

Cité par Sources :