1. General fully coupled FBSDES involving the value function and related nonlocal HJB equations combined with algebraic equations.
- Author
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Hao, Tao and Zhu, Qingfeng
- Subjects
- *
ALGEBRAIC equations , *VISCOSITY solutions , *EXISTENCE theorems , *DYNAMIC programming , *STOCHASTIC differential equations , *DIFFUSION coefficients , *HAMILTON-Jacobi-Bellman equation - Abstract
Recently, Hao and Li [Fully coupled forward-backward SDEs involving the value function. Nonlocal Hamilton–Jacobi–Bellman equations, ESAIM: Control Optim, Calc. Var.22 (2016) 519–538] studied a new kind of forward-backward stochastic differential equations (FBSDEs), namely the fully coupled FBSDEs involving the value function in the case where the diffusion coefficient σ in forward stochastic differential equations depends on control, but does not depend on z. In our paper, we generalize their work to the case where σ depends on both control and z , which is called the general fully coupled FBSDEs involving the value function. The existence and uniqueness theorem of this kind of equations under suitable assumptions is proved. After obtaining the dynamic programming principle for the value function W , we prove that the value function W is the minimum viscosity solution of the related nonlocal Hamilton–Jacobi–Bellman equation combined with an algebraic equation. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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