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20092023
most citedA proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations

153 citations · 899 across the 45 of their papers we have counts for

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Showing 2018 · math.FAShow all

2 papers · 2 filters

math.FA2018★ 97 cited

DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing

Dennis Elbrächter, Philipp Grohs, Arnulf Jentzen +1

We analyze approximation rates by deep ReLU networks of a class of multi-variate solutions of Kolmogorov equations which arise in option pricing. Key technical devices are deep ReL…

math.FA2018★ 16 cited

Gabor phase retrieval is severely ill-posed

Rima Alaifari, Philipp Grohs

The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This…