Sara Svaluto-Ferro - From signature-based models to affine and polynomial processes and back
|Dates:||15 February 2023|
|Times:||15:00 - 16:00|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
Sara Svaluto-Ferro (University of Verona) will speak in the Probability seminar. (online)
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. We also present methods for how to fit these models to data.
In the second part, we focus on signature SDEs, i.e. 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 over-parametrized dynamic models. We show that generic classes of diffusion models can be described in terms of a signature SDEs. This allows getting 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 and Josef Teichmann.
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