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We propose a methodology to approximate conditional distributions in theelliptope of correlation matrices based on conditional generative adversarialnetworks. We illustrate the methodology with an application from quantitativefinance: Monte Carlo simulations of correlated returns to compare risk-basedportfolio construction methods. Finally, we discuss about current limitationsand advocate for further exploration of the elliptope geometry to improveresults.

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