This repository contains implementations of randomized quasi-Monte Carlo (RQMC) methods with Fourier transform within both single-level and multilevel frameworks for exponential and QPC loss functions under Gaussian and normal inverse Gaussian (NIG) loss vectors.

The implementation is in the Python programming language and the notation in the code is consistent with the following works:

• Chiheb Ben Hammouda and Truong Ngoc Nguyen. Single- and Multi-Level Fourier-RQMC Methods for Multivariate Shortfall Risk (arXiv preprint).

In case of use of the code, please cite us by mentioning the webpage containing the code and adding the following references to your work:

@article{hammouda2026single,
  title={Single-and Multi-Level Fourier-RQMC Methods for Multivariate Shortfall Risk},
  author={Hammouda, Chiheb Ben and Nguyen, Truong Ngoc},
  journal={arXiv preprint arXiv:2602.06424},
  year={2026}
}