121 citations · 190 across the 14 of their papers we have counts for
19 papers
Dynamic Universal Approximation via Signature Controlled Differential Equations
Tomás Carrondo, Christa Cuchiero, Paul P. Hager +1
We study signature controlled differential equations (Sig-CDEs), that is, path-dependent controlled differential equations (CDEs) whose vector fields factor through the signature m…
Quantitative Halmos-Savage theorems and robust large financial markets
Christa Cuchiero, Irene Klein, Georg Köstenberger +1
We establish a quantitative version of the classical Halmos-Savage Theorem for convex, potentially non-dominated sets of probability measures and its dual counterpart, generalizing…
Robust financial calibration: a Bayesian approach for neural SDEs
Christa Cuchiero, Eva Flonner, Kevin Kurt
The paper presents a Bayesian framework for the calibration of financial models using neural stochastic differential equations (neural SDEs), for which we also formulate a global u…
Ramifications of generalized Feller theory
Christa Cuchiero, Tonio Möllmann, Josef Teichmann
Generalized Feller theory provides an important analog to Feller theory beyond locally compact state spaces. This is very useful for solutions of certain stochastic partial differe…
Global universal approximation of functional input maps on weighted spaces
Christa Cuchiero, Philipp Schmocker, Josef Teichmann
We introduce so-called functional input neural networks defined on a possibly infinite dimensional weighted space with values also in a possibly infinite dimensional output space.…
Risk measures under model uncertainty: a Bayesian viewpoint
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. Analyzing their…
Discrete-time signatures and randomness in reservoir computing
Christa Cuchiero, Lukas Gonon, Lyudmila Grigoryeva +2
A new explanation of geometric nature of the reservoir computing phenomenon is presented. Reservoir computing is understood in the literature as the possibility of approximating in…
A generative adversarial network approach to calibration of local stochastic volatility models
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. To ac…
Deep neural networks, generic universal interpolation, and controlled ODEs
Christa Cuchiero, Martin Larsson, Josef Teichmann
A recent paradigm views deep neural networks as discretizations of certain controlled ordinary differential equations, sometimes called neural ordinary differential equations. We m…
Markovian lifts of positive semidefinite affine Volterra type processes
Christa Cuchiero, Josef Teichmann
We consider stochastic partial differential equations appearing as Markovian lifts of matrix valued (affine) Volterra type processes from the point of view of the generalized Felle…
Generalized Feller processes and Markovian lifts of stochastic Volterra processes: the affine case
Christa Cuchiero, Josef Teichmann
We consider stochastic (partial) differential equations appearing as Markovian lifts of affine Volterra processes with jumps from the point of view of the generalized Feller proper…
A fundamental theorem of asset pricing for continuous time large financial markets in a two filtration setting
Christa Cuchiero, Irene Klein, Josef Teichmann
We present a version of the fundamental theorem of asset pricing (FTAP) for continuous time large financial markets with two filtrations in an -setting for $ 1 \leq p < \infty…
A new perspective on the fundamental theorem of asset pricing for large financial markets
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 fundame…
A convergence result for the Emery topology and a variant of the proof of the fundamental theorem of asset pricing
Christa Cuchiero, Josef Teichmann
We show that \emph{No unbounded profit with bounded risk} (NUPBR) implies \emph{predictable uniform tightness} (P-UT), a boundedness property in the Emery topology which has been i…
Fourier transform methods for pathwise covariance estimation in the presence of jumps
Christa Cuchiero, Josef Teichmann
We provide a new non-parametric Fourier procedure to estimate the trajectory of the instantaneous covariance process (from discrete observations of a multidimensional price process…
Affine processes on symmetric cones
Christa Cuchiero, Martin Keller-Ressel, Eberhard Mayerhofer +1
We consider affine Markov processes taking values in convex cones. In particular, we characterize all affine processes taking values in an irreducible symmetric cone in terms of ce…
Affine processes on positive semidefinite matrices
Christa Cuchiero, Damir Filipović, Eberhard Mayerhofer +1
This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been mot…
Polynomial processes and their applications to mathematical Finance
Christa Cuchiero, Martin Keller-Ressel, Josef Teichmann
We introduce a class of Markov processes, called -polynomial, for which the calculation of (mixed) moments up to order only requires the computation of matrix exponentials.…
Affine Models
Christa Cuchiero, Damir Filipovic, Josef Teichmann
Affine term structure models have gained significant attention in the finance literature, mainly due to their analytical tractability and statistical flexibility. The aim of this a…