Geodesic
Fully coupled forward-backward SDEs involving the value function and associated nonlocal Hamilton−Jacobi−Bellman equations
Hao, Tao1, 2 ; Li, Juan1
1 School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, P.R. China
2 School of Science and Technology, Shandong University of Traditional Chinese Medicine, Jinan 250355, P.R. China
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 2, pp. 519-538

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

A new type of controlled fully coupled forward-backward stochastic differential equations is discussed, namely those involving the value function. With a new iteration method, we prove an existence and uniqueness theorem of a solution for this type of equations. Using the notion of extended “backward semigroup”, we prove that the value function satisfies the dynamic programming principle and is a viscosity solution of the associated nonlocal Hamilton−Jacobi−Bellman equation.

Reçu le :
DOI : 10.1051/cocv/2015016
Classification : 60H10, 60H30, 35K65
Keywords: Fully coupled FBSDE involving value function, dynamic programming principle, fully coupled mean-field FBSDE, viscosity solution, nonlocal Hamilton−Jacobi−Bellman equation

Hao, Tao 1, 2 ; Li, Juan 1

1 School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, P.R. China
2 School of Science and Technology, Shandong University of Traditional Chinese Medicine, Jinan 250355, P.R. China 
@article{COCV_2016__22_2_519_0,
     author = {Hao, Tao and Li, Juan},
     title = {Fully coupled forward-backward {SDEs} involving the value function and associated nonlocal {Hamilton\ensuremath{-}Jacobi\ensuremath{-}Bellman} equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {519--538},
     publisher = {EDP-Sciences},
     volume = {22},
     number = {2},
     year = {2016},
     doi = {10.1051/cocv/2015016},
     zbl = {1338.60146},
     mrnumber = {3491781},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015016/}
}
TY  - JOUR
AU  - Hao, Tao
AU  - Li, Juan
TI  - Fully coupled forward-backward SDEs involving the value function and associated nonlocal Hamilton−Jacobi−Bellman equations
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2016
SP  - 519
EP  - 538
VL  - 22
IS  - 2
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015016/
DO  - 10.1051/cocv/2015016
LA  - en
ID  - COCV_2016__22_2_519_0
ER  - 
%0 Journal Article
%A Hao, Tao
%A Li, Juan
%T Fully coupled forward-backward SDEs involving the value function and associated nonlocal Hamilton−Jacobi−Bellman equations
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2016
%P 519-538
%V 22
%N 2
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015016/
%R 10.1051/cocv/2015016
%G en
%F COCV_2016__22_2_519_0
Hao, Tao; Li, Juan. Fully coupled forward-backward SDEs involving the value function and associated nonlocal Hamilton−Jacobi−Bellman equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 2, pp. 519-538. doi: 10.1051/cocv/2015016

Cité par Sources :