Abstract: Generative adversarial networks (GANs) have been extremely successful in generating samples, from seemingly high dimensional probability measures. However, these methods struggle to capture the temporal dependence of joint probability distributions induced by time-series data. Furthermore, long time-series data streams hugely increase the dimension of the target space, which may render generative modelling infeasible. To overcome these challenges, motivated by the autoregressive models in econometric, we are interested in the conditional distribution of future time series given the past information. In this talk, we propose the generic conditional Sig-WGAN framework by integrating Wasserstein-GANs (WGANs) with mathematically principled and efficient path feature extraction called the signature of a path. The signature feature space enables the explicit representation of the proposed discriminators which alleviates the need for expensive training. We validate our method on both synthetic and empirical financial dataset to demonstrate the strength of our method compared with other state-of-the-art benchmarks.

Bio: Hao Ni is an associate professor in financial mathematics at University College London (UCL) and the Turing Fellow at the Alan Turing institute since September 2016. Prior to this, she was a visiting postdoctoral researcher at ICERM and Department of Applied Mathematics at Brown University from September 2012 to May 2013. She continued her postdoctoral research at the Oxford-Man Institute of Quantitative Finance until 2016. She finished her D.Phil. in Mathematics at the University of Oxford.

Her research interests include stochastic analysis, financial mathematics and machine learning. More specifically, she is interested in non-parametric modelling effects of complex multi-modal data streams through rough paths theory and machine learning. Moreover, she has research interests in real-world applications, such as human-computer interface, computer vision and quantitative finance.

Meeting Recording: https://ucsb.zoom.us/rec/share/WGhtTeVF2jvreQiNhKYocrl_j64Yk9Q6SbyYxHE4kOACCVJtClRPP95ZORjuv8ia.p6qDfdvEvKrvFITX

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