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In this paper, we introduce various machine learning solvers for (coupled)forward-backward systems of stochastic differential equations (FBSDEs) drivenby a Brownian motion and a Poisson random measure. We provide a rigorouscomparison of the different algorithms and demonstrate their effectiveness invarious applications, such as cases derived from pricing with jumps andmean-field games. In particular, we show the efficiency of the deep-learningalgorithms to solve a coupled multi-dimensional FBSDE system driven by atime-inhomogeneous jump process with stochastic intensity, which describes theNash equilibria for a specific mean-field game (MFG) problem for which we alsoprovide the complete theoretical resolution. More precisely, we develop anextension of the MFG model for smart grids introduced in Alasseur, Campi,Dumitrescu and Zeng (Annals of Operations Research, 2023) to the case when therandom jump times correspond to the jump times of a doubly Poisson process. Wefirst provide an existence result of an equilibria and derive its semi-explicitcharacterization in terms of a system of FBSDEs in the linear-quadraticsetting. We then compare the MFG solution to the optimal strategy of a centralplanner and provide several numerical illustrations using the deep-learningsolvers presented in the first part of the paper.

Deep learning algorithms for FBSDEs with jumps: Applications to option pricing and a MFG model for smart grids