Search Results for author: Lukas Gonon

Found 13 papers, 1 papers with code

Expressive Power of Randomized Signature

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.

Transfer Learning

Neural network approximation for superhedging prices

no code implementations29 Jul 2021 Francesca Biagini, Lukas Gonon, Thomas Reitsam

First we prove that the $\alpha$-quantile hedging price converges to the superhedging price at time $0$ for $\alpha$ tending to $1$, and show that the $\alpha$-quantile hedging price can be approximated by a neural network-based price.

Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality

no code implementations14 Jun 2021 Lukas Gonon

We derive bounds for the prediction error of random neural networks for learning sufficiently non-degenerate Black-Scholes type models.

Deep ReLU neural networks overcome the curse of dimensionality for partial integrodifferential equations

no code implementations23 Feb 2021 Lukas Gonon, Christoph Schwab

Deep neural networks (DNNs) with ReLU activation function are proved to be able to express viscosity solutions of linear partial integrodifferental equations (PIDEs) on state spaces of possibly high dimension $d$.

Numerical Analysis Numerical Analysis Probability

Fading memory echo state networks are universal

no code implementations22 Oct 2020 Lukas Gonon, Juan-Pablo Ortega

Echo state networks (ESNs) have been recently proved to be universal approximants for input/output systems with respect to various $L ^p$-type criteria.

Discrete-time signatures and randomness in reservoir computing

no code implementations17 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.

Weak error analysis for stochastic gradient descent optimization algorithms

no code implementations3 Jul 2020 Aritz Bercher, Lukas Gonon, Arnulf Jentzen, Diyora Salimova

In applications one is often not only interested in the size of the error with respect to the objective function but also in the size of the error with respect to a test function which is possibly different from the objective function.

Face Recognition Fraud Detection

Memory and forecasting capacities of nonlinear recurrent networks

no code implementations22 Apr 2020 Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega

The notion of memory capacity, originally introduced for echo state and linear networks with independent inputs, is generalized to nonlinear recurrent networks with stationary but dependent inputs.

Time Series

Approximation Bounds for Random Neural Networks and Reservoir Systems

no code implementations14 Feb 2020 Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega

This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights.

Uniform error estimates for artificial neural network approximations for heat equations

no code implementations20 Nov 2019 Lukas Gonon, Philipp Grohs, Arnulf Jentzen, David Kofler, David Šiška

These mathematical results from the scientific literature prove in part that algorithms based on ANNs are capable of overcoming the curse of dimensionality in the numerical approximation of high-dimensional PDEs.

Risk bounds for reservoir computing

no code implementations30 Oct 2019 Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega

We analyze the practices of reservoir computing in the framework of statistical learning theory.

Learning Theory

Reservoir Computing Universality With Stochastic Inputs

no code implementations7 Jul 2018 Lukas Gonon, Juan-Pablo Ortega

The universal approximation properties with respect to $L ^p $-type criteria of three important families of reservoir computers with stochastic discrete-time semi-infinite inputs is shown.

Deep Hedging

2 code implementations8 Feb 2018 Hans Bühler, Lukas Gonon, Josef Teichmann, Ben Wood

We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep reinforcement machine learning methods.

Computational Finance Numerical Analysis Optimization and Control Probability Risk Management 91G60, 65K99

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