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-boxformat. We construct a generative neural network, whose loss function exploitsa specific representation of the Maximum-Mean-Discrepancy metric to directlyincorporate the targeted characteristic function. The construction is universalin the sense that it is independent of the dimension and that it does notrequire any assumptions on the given characteristic function. Furthermore,finite sample guarantees on the approximation quality in terms of theMaximum-Mean Discrepancy metric are derived. The method is illustrated in ashort simulation study.