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.

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
Mots clés : 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
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     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},
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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://www.numdam.org/articles/10.1051/cocv/2015016/

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