Volume 22, Number 2, April-June 2016
|Page(s)||519 - 538|
|Published online||06 April 2016|
Fully coupled forward-backward SDEs involving the value function and associated nonlocal Hamilton−Jacobi−Bellman equations∗
1 School of Mathematics and Statistics,
Shandong University, Weihai, Weihai
2 School of Science and Technology, Shandong University of Traditional Chinese Medicine, Jinan 250355, P.R. China
Revised: 24 November 2014
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.
Mathematics Subject Classification: 60H10 / 60H30 / 35K65
Key words: Fully coupled FBSDE involving value function / dynamic programming principle / fully coupled mean-field FBSDE / viscosity solution / nonlocal Hamilton−Jacobi−Bellman equation
© EDP Sciences, SMAI 2016
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