Generative neural networks for characteristic functions

In this work, we provide a simulation algorithm to simulate from a (multivariate) characteristic function, which is only accessible in a black-box format. We construct a generative neural network, whose loss function exploits a specific representation of the Maximum-Mean-Discrepancy metric to directly incorporate the targeted characteristic function. The construction is universal in the sense that it is independent of the dimension and that it does not require any assumptions on the given characteristic function. Furthermore, finite sample guarantees on the approximation quality in terms of the Maximum-Mean Discrepancy metric are derived. The method is illustrated in a short simulation study.