  This paper examines an efficient method for quasi-random sampling of copulas
in Monte Carlo computations. Traditional methods, like conditional distribution
methods (CDM), have limitations when dealing with high-dimensional or implicit
copulas, which refer to those that cannot be accurately represented by existing
parametric copulas. Instead, this paper proposes the use of generative models,
such as Generative Adversarial Networks (GANs), to generate quasi-random
samples for any copula. GANs are a type of implicit generative models used to
learn the distribution of complex data, thus facilitating easy sampling. In our
study, GANs are employed to learn the mapping from a uniform distribution to
copulas. Once this mapping is learned, obtaining quasi-random samples from the
copula only requires inputting quasi-random samples from the uniform
distribution. This approach offers a more flexible method for any copula.
Additionally, we provide theoretical analysis of quasi-Monte Carlo estimators
based on quasi-random samples of copulas. Through simulated and practical
applications, particularly in the field of risk management, we validate the
proposed method and demonstrate its superiority over various existing methods.
