1 code implementation • 3 Oct 2023 • Christa Cuchiero, Janka Möller
We prove that these portfolios are universal in the sense that every continuous, possibly path-dependent, portfolio function of the market weights can be uniformly approximated by signature portfolios.
1 code implementation • 5 Jun 2023 • Christa Cuchiero, Philipp Schmocker, Josef Teichmann
This then applies in particular to approximation of (non-anticipative) path space functionals via functional input neural networks.
1 code implementation • 30 Jan 2023 • Christa Cuchiero, Guido Gazzani, Janka Möller, Sara Svaluto-Ferro
Adding to such a primary process the Brownian motion driving the stock price, allows then to express both the log-price and the VIX squared as linear functions of the signature of the corresponding augmented process.
no code implementations • 17 Oct 2022 • Christa Cuchiero, Luca Di Persio, Francesco Guida, Sara Svaluto-Ferro
We introduce a framework that allows to employ (non-negative) measure-valued processes for energy market modeling, in particular for electricity and gas futures.
1 code implementation • 26 Jul 2022 • Christa Cuchiero, Guido Gazzani, Sara Svaluto-Ferro
We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional continuous semimartingale.
no code implementations • 14 Apr 2022 • Christa Cuchiero, Guido Gazzani, Irene Klein
We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property.
no code implementations • NeurIPS Workshop DLDE 2021 • Christa Cuchiero, Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega, Josef Teichmann
We consider the question whether the time evolution of controlled differential equations on general state spaces can be arbitrarily well approximated by (regularized) regressions on features generated themselves through randomly chosen dynamical systems of moderately high dimension.
no code implementations • 17 Sep 2020 • Christa Cuchiero, Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega, Josef Teichmann
A new explanation of geometric nature of the reservoir computing phenomenon is presented.
1 code implementation • 5 May 2020 • Christa Cuchiero, Wahid Khosrawi, Josef Teichmann
We propose a fully data-driven approach to calibrate local stochastic volatility (LSV) models, circumventing in particular the ad hoc interpolation of the volatility surface.
no code implementations • 23 Dec 2014 • Christa Cuchiero, Irene Klein, Josef Teichmann
In the context of large financial markets we formulate the notion of \emph{no asymptotic free lunch with vanishing risk} (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an (even uncountably) infinite number of assets, as it is for instance the case in bond markets.