On optimal control of coupled mean-field forward-backward stochastic equations
-
Badreddine Mansouri
,
Brahim Mezerdi
and
Khaled Bahlali
Abstract
We consider a control problem for a mean-field coupled forward-backward stochastic differential equations, called also McKean–Vlasov equation (MF-FBSDE). For this type of equations, the coefficients depend not only on the state of the system, but also on its marginal distributions. They arise naturally in mean-field control problems and mean-field games. We consider the relaxed control problem where admissible controls are measure-valued processes. We prove the existence of a relaxed optimal control by using a suitable form of Skorokhod representation theorem and Jakubowski’s topology, on the space of càdlàg functions. We use martingale measure to define the relaxed state process. Our results extend to MF-FBSDEs those already known for forward and backward stochastic equations of Itô type.
Funding statement: The second author would like to acknowledge the support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum and Minerals, KSA (KFUPM), for funding this work through Project No. SB 201017.
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Articles in the same Issue
- Frontmatter
- Existence results for a coupled system of fractional stochastic differential equations involving Hilfer derivative
- Minimax interpolation of continuous time stochastic processes with periodically correlated increments observed with noise
- On optimal control of coupled mean-field forward-backward stochastic equations
- Double sequences of complex uncertain variables associated with multiplier sequences
- The estimator G 59 for the solutions of the regularized Kolmogorov--Wiener filter
- Canonical equation K 107 for symmetric matrix with independent zebra random lines
- Existence of a weak solution to a Markovian BSDE with discontinuous coefficients
- Generalized delay BSDE driven by fractional Brownian motion
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Articles in the same Issue
- Frontmatter
- Existence results for a coupled system of fractional stochastic differential equations involving Hilfer derivative
- Minimax interpolation of continuous time stochastic processes with periodically correlated increments observed with noise
- On optimal control of coupled mean-field forward-backward stochastic equations
- Double sequences of complex uncertain variables associated with multiplier sequences
- The estimator G 59 for the solutions of the regularized Kolmogorov--Wiener filter
- Canonical equation K 107 for symmetric matrix with independent zebra random lines
- Existence of a weak solution to a Markovian BSDE with discontinuous coefficients
- Generalized delay BSDE driven by fractional Brownian motion
- Stochastic integration respect a cylindrical martingale-Lévy process with second moments
