Abstract: Generative Adversarial Networks (GANs) have proven to be a powerful framework for learning to draw samples from complex distributions. In this talk I will discuss the challenge of learning sequential data via GANs. This notably requires the choice of a loss function that reflects the discrepancy between (measures on) paths. To take on this task, we employ adapted versions of optimal transport distances, that result from imposing a temporal causality constraint on classical transport problems. This constraint provides a natural framework to parameterize the cost function that is learned by the discriminator as a robust (worst-case) distance. Following Genevay et al. (2018), we include an entropic penalization term which allows for the use of the Sinkhorn algorithm when computing the optimal transport cost. In particular, I will present a learning architecture for market generation that is consistent with both the observed spot prices and the market prices of derivatives. Here a conditional GAN structure will be used to learn the evolution of asset prices, while derivative prices will be used to learn the change of measure from the real-world measure to the pricing one.

This talk is based on a joint work with F.Krach.

Bio: Beatrice Acciaio is Professor of Mathematics at ETH Zurich since 2020. Before joining ETH, Beatrice was associate professor at the London School of Economics, and prior to that she has been part of several research groups, at the Technical University of Vienna, the University of Perugia, and the University of Vienna. Beatrice completed her PhD in 2006 under the supervision of Walter Schachermayer.

Beatrice's main areas of research are mathematical finance, probability, and optimal transport.

Beatrice is member of the Council of the Bachelier Finance Society, she is Associate Editor for the SIAM Journal on Financial Mathematics, for Finance and Stochastics, for Mathematical Finance, and for the Bocconi & Springer Series on Mathematics, Statistics, Finance and Economics.

Meeting Recording: https://ucsb.zoom.us/rec/share/T4L7M_ZTyDlzJDozlkNFdiTeC_VqJFU0pRPLREyc8XNAf214dBSCcDnOZtf4xdKo.-tgbGnYL4nLZFitZ

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