Séminaire du CIMMUL – Huyên Pham

Generative modeling for time series via Schrödinger bridge

Huyên Pham

Professeur
Université de Paris Diderot

Résumé

We propose a novel generative model for time series based on Schr\ »odinger bridge (SB) approach. This consists in the entropic interpolation via 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 resulting solution is described by a stochastic differential equation over a  finitehorizon with a path-dependent drift function, which accurately captures  the temporal dynamics of the time series distribution.

We estimate the drift function from data samples by kernel regression methods, which is particularly practical and computationally low-cost, and the simulation of the SB diffusion yields new synthetic data samples of the time series.

The performance of our generative model is evaluated through a series of numerical experiments.  First, we test with a GARCH Model, and the example of fractional Brownian motion, and measure the accuracy of our algorithm with marginal and temporal dependencies metrics. Next, we use our SB generated synthetic samples for the application to deep hedging on real-data sets.

Le séminaire aura lieu au local 2870 du pavillon Alexandre-Vachon et en ligne.

Pour rejoindre la réunion Zoom :
https://ulaval.zoom.us/j/62680136430?pwd=eldBYjdNTG5QR2VxTTFqbVM4UGVRZz09

Meeting ID: 626 8013 6430
Passcode: 693150