Dear colleagues,

it is our pleasure to invite you to the following online seminar:

Zoom link (see also details below): https://us02web.zoom.us/j/88398874167?pwd=YkRzdlNYWjVjUlc3T294ZjZuVHNSdz09 https://us02web.zoom.us/j/88398874167?pwd=YkRzdlNYWjVjUlc3T294ZjZuVHNSdz09

Speaker: https://homepage.univie.ac.at/sara.svaluto-ferro/ Sara Svaluto-Ferro (University of Vienna)

Title: From signature-based models to affine and polynomial processes and back.

Time: Tuesday, April 27, 4PM (Italian time)

Abstract: Modern universal classes of dynamic processes, based on neural networks or signature methods, have recently entered the field of stochastic modeling, in particular in Mathematical Finance. This has opened the door to more data-driven and thus more robust model selection mechanisms, while principles like no arbitrage still apply. We analyze here different types of signature models.

In the first part, we focus on models based on the signature of a supporting process, which can range from a Brownian motion, to a multidimensional Levy-process, to a general multidimensional tractable stochastic process, to the times series corresponding to some liquid objects on the market. We also present methods how to fit these models to data.

In the second part we focus on signature SDEs, i.e. (possibly Lévy driven) SDEs whose characteristics are linear functions of the process’ signature. We show how these new models can be embedded in the framework of affine and polynomial processes, which have been - due to their tractability - the dominating process class prior to the new era of highly overparametrized dynamic models. We show that generic classes of diffusion models can be described in terms of a signature SDEs. This allows to get power series expansions for expected values of analytic functions of the process' marginals.

The talk is based on joint works with Christa Cuchiero, Guido Gazzani, Francesca Primavera and Josef Teichmann.

Zoom meeting details:

meeting ID: 883 9887 4167

Passcode: mVJ6SR

Best,

Matteo Burzoni