Dear Colleagues,

We would like to invite you to the following (double) SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi (abstracts below):

*Signature-based models: theory and calibration * by *Sara Svaluto Ferro* (Università di Verona)

*Noise-induced oscillations for the mean-field dissipative contact process* by* Elisa Marini* (Università degli Studi di Padova)

The seminars will take place on *TUE, 4.6.2024* respectively at *14:00 CET *in Aula Seminari, Dipartimento di Matematica, UNIPI *and 15:00 CET* in Aula Tricerri, Dipartimento di Matematica e Informatica "Ulisse Dini", UNIFI and both streamed online at this link https://meet.google.com/gji-phwo-vbg.

The organizers, A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco https://sites.google.com/unipi.it/spass https://www.google.com/url?q=https://sites.google.com/unipi.it/spass&source=gmail-imap&ust=1665669490000000&usg=AOvVaw07o0tKOUGmZjDDF2Ta7pQY

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*Signature-based models: theory and calibration *

*Abstract: Universal classes of dynamic processes based on neural networks and signature methods have recently entered the area of stochastic modeling and Mathematical Finance. This has opened the door to robust and more data-driven model selection mechanisms, while first principles like no arbitrage still apply.In the first part of the talk we focus on signature SDEs whose characteristics are linear functions of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional tractable stochastic process. The framework is universal in the sense that classical models can be approximated arbitrarily well and that the model characteristics can be learned from all sources of available data by simple methods. Indeed, we derive formulas for the expected signature in terms of the expected signature of the primary underlying process.In the second part we focus on a stochastic volatility model where the dynamics of the volatility are described by linear functions of the (time extended) signature of a primary process. Under the additional assumption that this primary process is of polynomial type, we obtain closed form expressions for the squared VIX by exploiting the fact that the truncated signature of a polynomial process is again a polynomial process. Adding to such a primary process the Brownian motion driving the stock price, allows then to express both the log-price and the squared VIX as linear functions of the signature of the corresponding augmented process. For both SPX and VIX options we obtain highly accurate calibration results.The talk is based on joint works with Christa Cuchiero, Guido Gazzani, and Janka Möller.*

*Noise-induced oscillations for the mean-field dissipative contact process*

*Abstract: In this talk, we will introduce a dissipative version of the contact process with mean-field interaction admitting a simple epidemiological interpretation. In particular, we will focus on the thermodynamic limit of the process, providing a law of large numbers (propagation of chaos) and a central limit theorem for the corresponding normal fluctuations.These results reveal that it is the noise, which is only present in the finite-size system and is internal to the system, that induces persistent oscillatory behaviors reminiscent of the emergence of pandemic waves in real epidemics.*