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- W4366998496 abstract "Abstract In this paper, we study a nonzero-sum stochastic differential game for a system whose dynamics is governed by a mean-field forward-backward stochastic differential equation (MF-FBSDE) with delay and noisy memory. We transform the stochastic game into a set of stochastic optimal control problems. By applying Variational method and using Malliavin calculus, we establish the sufficient and necessary maximum principles of controls, so that all players are in Nash equilibrium in the game. Based on this, the optimal strategy for solving this kind of stochastic differential game problem is provided. We apply the result to finance, and consider the optimal consumption model in a financial market with delay and noisy memory that maximizes the recursive utility of each player in the Nash equilibrium. The numerical results illustrate the influences of mean-field, delay and noisy memory on the optimal recursive utilities of the players in the game. In addition, we give the proof of the existence and uniqueness of the solution of this new type of MF-FBSDE system under certain assumptions, and discuss the solution of its adjoint FBSDE system involving Malliavin derivatives." @default.
- W4366998496 created "2023-04-27" @default.
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- W4366998496 date "2023-04-25" @default.
- W4366998496 modified "2023-10-08" @default.
- W4366998496 title "Optimal strategy of mean-field FBSDE games with delay and noisy memory based on Malliavin calculus" @default.
- W4366998496 doi "https://doi.org/10.21203/rs.3.rs-2843308/v1" @default.
- W4366998496 hasPublicationYear "2023" @default.
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