Lukas Gonon
39 results
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Item type:Publication, Universal Approximation Theorem and Error Bounds for Quantum Neural Networks and Quantum Reservoirs(2025); Antoine JacquierType:journal articleJournal:IEEE Transactions on Neural Networks and Learning SystemsScopus© Citations 9 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Reservoir Kernels and Volterra Series(2025); ; Type:journal articleJournal:IEEE Transactions on Neural Networks and Learning SystemsScopus© Citations 2 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations(2024-12); Arnulf JentzenType:journal articleJournal:Partial Differential Equations and ApplicationsScopus© Citations 5 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Detecting asset price bubbles using deep learning(2024-07-18); Scopus© Citations 2 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Approximation Rates for Deep Calibration of (Rough) Stochastic Volatility Models(2024-09-30); Niklas WalterType:journal articleJournal:SIAM Journal on Financial Mathematics - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Deep neural network expressivity for optimal stopping problems(2024-07)<jats:title>Abstract</jats:title><jats:p>This article studies deep neural network expression rates for optimal stopping problems of discrete-time Markov processes on high-dimensional state spaces. A general framework is established in which the value function and continuation value of an optimal stopping problem can be approximated with error at most <jats:inline-formula><jats:alternatives><jats:tex-math>$\varepsilon $</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ε</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> by a deep ReLU neural network of size at most <jats:inline-formula><jats:alternatives><jats:tex-math>$\kappa d^{\mathfrak{q}} \varepsilon ^{-\mathfrak{r}}$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>κ</mml:mi> <mml:msup> <mml:mi>d</mml:mi> <mml:mi>q</mml:mi> </mml:msup> <mml:msup> <mml:mi>ε</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi>r</mml:mi> </mml:mrow> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula>. The constants <jats:inline-formula><jats:alternatives><jats:tex-math>$\kappa ,\mathfrak{q},\mathfrak{r} \geq 0$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>κ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>r</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:math></jats:alternatives></jats:inline-formula> do not depend on the dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$d$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>d</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> of the state space or the approximation accuracy <jats:inline-formula><jats:alternatives><jats:tex-math>$\varepsilon $</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ε</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>. This proves that deep neural networks do not suffer from the curse of dimensionality when employed to approximate solutions of optimal stopping problems. The framework covers for example exponential Lévy models, discrete diffusion processes and their running minima and maxima. These results mathematically justify the use of deep neural networks for numerically solving optimal stopping problems and pricing American options in high dimensions.</jats:p>Type:journal articleJournal:Finance and StochasticsScopus© Citations 4 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Scopus© Citations 12 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Neural network approximation for superhedging prices(2023-01); Thomas Reitsam<jats:title>Abstract</jats:title><jats:p>This article examines neural network‐based approximations for the superhedging price process of a contingent claim in a discrete time market model. First we prove that the α‐quantile hedging price converges to the superhedging price at time 0 for α tending to 1, and show that the α‐quantile hedging price can be approximated by a neural network‐based price. This provides a neural network‐based approximation for the superhedging price at time 0 and also the superhedging strategy up to maturity. To obtain the superhedging price process for , by using the Doob decomposition, it is sufficient to determine the process of consumption. We show that it can be approximated by the essential supremum over a set of neural networks. Finally, we present numerical results.</jats:p>Type:journal articleJournal:Mathematical FinanceScopus© Citations 4 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Approximation bounds for random neural networks and reservoir systems(Institute of Mathematical Statistics, 2023-02); ; Type:journal articleJournal:The Annals of Applied ProbabilityVolume:33Issue:1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Random Feature Neural Networks Learn Black-Scholes Type PDEs Without Curse of Dimensionality(2023)Type:journal articleJournal:Journal of Machine Learning Research