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Creators/Authors contains: "JP Fouque, Zaoyu Zhang"

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  1. (, Frontiers in applied mathematics and statistics)
    We consider a general class of mean field control problems described by stochastic delayed differential equations of McKean-Vlasov type. Two numerical algorithms are provided based on deep learning techniques, one is to directly parameterizing the optimal control using neural networks, the other is based on numerically solving the McKean-Vlasov forward anticipated backward stochastic differential equation (MV-FABSDE) system. In addition, we establish the necessary and sufficient stochastic maximum principle of this class of mean field control problems with delay based on the differential calculus on function of measures, and the exis- tence and uniqueness results are proved for the associated MV-FABSDE system under suitable conditions. 
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    Full Text Available 
  2. (, Risks)
    We study a toy model of linear-quadratic mean field game with delay. We “lift" the delayed dynamic into an infinite dimensional space, and recast the mean field game system which is made of a forward Kolmogorov equation and a backward Hamilton-Jacobi-Bellman equation. We identify the corresponding master equation. A solution to this master equation is computed, and we show that it provides an approximation to a Nash equilibrium of the finite player game. 
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    Accepted Manuscript Full Text Available