Abstract: We propose a novel generative model for time series based on Schrödinger bridge (SB) type diffusion. This consists in the interpolation via entropic optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, which can be  estimated  from data samples by nonparametric, e.g. kernel regression methods.  The simulation of the SB diffusion then yields new synthetic data samples of the time series. The performance of our generative model is evaluated through a series of numerical experiments on simulated datasets including the examples of autoregressive models,  GARCH Model, and  fractional Brownian motion,  and  the accuracy of our algorithm is measured  with marginal, temporal dependencies metrics, and predictive scores. We also use our SB generated synthetic samples for the application to deep hedging on real-data sets.  

bio: Huyên PHAM is Distinguished  Professor of Mathematics at Université Paris Cité.  He leads research in  stochastic analysis and control, quantitative finance, and machine learning, and is the author of more than 110 publications, including the monograph Continuous time Stochastic Control and Optimization with Financial Applications.  He is the vice-president of the Bachelier Finance Society, and serves currently as the  Editor-in Chief of the journal SIAM Journal on Control and Optimization.  

Prof. Pham was appointed member of the Institut Universitaire de France in 2006, awarded the Louis Bachelier prize by the French Academy of Sciences in 2007, and was a plenary speaker at the 9th World congress of the Bachelier Finance Society in 2016, and at the 6th Asian Quantitative Finance Conference in 2018. 

Zoom Meeting: https://us06web.zoom.us/j/83231466990?pwd=pK6GFsgtpY6dTRuLjtADjXfsNPSNfb.1

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