ON THE REGULARITY OF SLE TRACE

Autor: PETER K. FRIZ, HUY TRAN

Publikováno v: Forum of Mathematics, Sigma, Vol 5 (2017)

We revisit regularity of SLE trace, for all $\unicode[STIX]{x1D705}\neq 8$ , and establish Besov regularity under the usual half-space capacity parametrization. With an embedding theorem of Garsia–Rodemich–Rumsey type, we obtain finite moments (

Externí odkaz: https://doaj.org/article/0143d76175ea4f9d99415da514561bae

Reconstructing Volatility: Pricing of Index Options under Rough Volatility

Autor: Peter K. Friz, Thomas Wagenhofer

In previous works Avellaneda et al. pioneered the pricing and hedging of index options - products highly sensitive to implied volatility and correlation assumptions - with large deviations methods, assuming local volatility dynamics for all component

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::29dae1e0b19ba82f3f1e5b624ced8d5d
http://arxiv.org/abs/2212.07817

Smooth Rough Paths, Their Geometry and Algebraic Renormalization

Autor: Carlo Bellingeri, Peter K. Friz, Sylvie Paycha, Rosa Preiß

We introduce the class of "smooth rough paths" and study their main properties. Working in a smooth setting allows us to discard sewing arguments and focus on algebraic and geometric aspects. Specifically, a Maurer-Cartan perspective is the key to a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::81121ca86fa23aa9bc4824c7cca1c1da
https://depositonce.tu-berlin.de/handle/11303/17196

Precise asymptotics: Robust stochastic volatility models

Autor: Paul Gassiat, Peter K. Friz, Paolo Pigato

Publikováno v: Annals of Applied Probability
Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2021, ⟨10.1214/20-AAP1608⟩
The Annals of Applied Probability

We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b483cd4b967bc6efe449d734ae8e2678
https://hdl.handle.net/2108/311643

Transport and continuity equations with (very) rough noise

Autor: Peter K. Friz, Nikolas Tapia, Ana Djurdjevac, Carlo Bellingeri

Existence and uniqueness for rough flows, transport and continuity equations driven by general geometric rough paths are established.
20 pages

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2b8aa2b15952fb3dc9b30773299700f4
http://arxiv.org/abs/2002.10432