cCorrGAN: Conditional Correlation GAN for Learning Empirical Conditional Distributions in the Elliptope

@article{Marti2021cCorrGANCC,
  title={cCorrGAN: Conditional Correlation GAN for Learning Empirical Conditional Distributions in the Elliptope},
  author={Gautier Marti and Victor Goubet and Frank Nielsen},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.10606}
}
We propose a methodology to approximate conditional distributions in the elliptope of correlation matrices based on conditional generative adversarial networks. We illustrate the methodology with an application from quantitative finance: Monte Carlo simulations of correlated returns to compare risk-based portfolio construction methods. Finally, we discuss about current limitations and advocate for further exploration of the elliptope geometry to improve results. 

Theoretically and computationally convenient geometries on full-rank correlation matrices

In contrast to SPD matrices, few tools exist to perform Riemannian statistics on the open elliptope of full-rank correlation matrices. The quotient-affine metric was recently built as the quotient of

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