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DTSTAMP:20260406T074840Z
UID:1605025800@ist.ac.at
DTSTART:20201110T173000
DTEND:20201110T181500
DESCRIPTION:Speaker: Christa Cuchiero\nhosted by M. Beiglböck\, N. Beresty
 cki\, L. Erdös\, J. Maas\, F. Toninelli\nAbstract: e elaborate on univers
 al properties of affine and polynomial processes. In several recent works 
 we could show that many models which are at first sight not recognized as 
 affine or polynomial can nevertheless be embedded in this framework via in
 finite dimensional lifts. For instance\, essentially all examples of (roug
 h) stochastic volatility models in mathematical finance can be viewed as i
 nfinite dimensional affine or polynomial processes.  Moreover\, all well-
 known measure-valued diffusions in population genetics such as the Fleming
 –Viot process\, the Super–Brownian motion\, and the Dawson–Watanabe 
 superprocess are affine or polynomial.  This suggests an inherent univers
 ality of these model classes. We try to make this mathematically precise b
 y showing that generic classes of diffusion models  are projections of in
 finite dimensional affine processes (which in this setup coincide with po
 lynomial processes). A key ingredient to establish this result is the sign
 ature process\, well known from rough paths theory. This then allows to ge
 t (formal) power series expansions for the Laplace transform/characteristi
 c function of large classes of stochastic processes via duality methods\, 
 which are well know from classical (finite dimensional) affine and polynom
 ial processes. The talk is based on  joint works with Sara Svaluto-Ferro 
 and Josef Teichmann.
LOCATION:Online via Zoom\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Christa Cuchiero: Universality of affine and polynomial processes
URL:https://talks-calendar.ista.ac.at/events/2898
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