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DTSTAMP:20241106T220844Z
UID:670cfaca1240b527965897@ist.ac.at
DTSTART:20241112T160000
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DESCRIPTION:Speaker: Christa Cuchiero\nhosted by Marco Mondelli\nAbstract:
Signature methods represent a non-parametric way for extracting characteri
stic features from time series data which is essential in machine learning
tasks\, dynamic stochastic modeling\, and mathematical finance. Indeed\,
signature based approaches allow for data-driven and thus more robust mode
l selection mechanisms\, while first principles (coming e.g. from physics)
can still be guaranteed.One focus of this talk lies on the use of signatu
re as universal linear regression basis of continuous paths functionals fo
r applications in stochastic modeling. In these applications key quantitie
s that have to be computed efficiently are the expected signature or the c
haracteristic function of the signature of some underlying stochastic proc
ess. Surprisingly this can be achieved for generic classes of (jump-)diffu
sions\, called signature-SDEs (with possibly path dependent characteristic
s)\, via techniques from so-called affine and polynomial processes. More p
recisely\, we show how the signature process of these diffusions can be em
bedded in the framework of affine and polynomial processes and how the inf
inite dimensional Feynman Kac PDE can be reduced to an ODE either of Ricca
ti or linear type. In terms of concrete applications we show a portfolio s
election problem which can be reduced to a convex quadratic optimization p
roblem due to the linear structure of the signature feature set.At the end
we present some new research directions\, including novel architectures w
here signature is combined with attention mechanisms\, generative adversar
ial approaches to time series generation based on signature SDEs and neura
l signature kernel learning.The talk is based on joint works with Janka Ml
ler\, Francesca Primavera\, Sara-Svaluto Ferro and Josef Teichmann.
LOCATION:Sunstone Bldg / Ground floor / Big Seminar Room A / 27 seats (I23.
EG.102)\, ISTA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Christa Cuchiero: (Neural)-signature methods\, applications in fina
nce and some research questions
URL:https://talks-calendar.ista.ac.at/events/5338
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