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.
DOI : 10.1051/cocv/2015016
Mots clés : Fully coupled FBSDE involving value function, dynamic programming principle, fully coupled mean-field FBSDE, viscosity solution, nonlocal Hamilton−Jacobi−Bellman equation
@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://archive.numdam.org/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://archive.numdam.org/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://archive.numdam.org/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. http://archive.numdam.org/articles/10.1051/cocv/2015016/
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