Neural network expression rates and applications of the deep parametric PDE method in counterparty credit risk

Kathrin Glau () and Linus Wunderlich ()
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Kathrin Glau: Queen Mary University of London
Linus Wunderlich: Queen Mary University of London

Annals of Operations Research, 2024, vol. 336, issue 1, No 11, 357 pages

Abstract: Abstract The recently introduced deep parametric PDE method combines the efficiency of deep learning for high-dimensional problems with the reliability of classical PDE models. The accuracy of the deep parametric PDE method is determined by the best-approximation property of neural networks. We provide (to the best of our knowledge) the first approximation results, which feature a dimension-independent rate of convergence for deep neural networks with a hyperbolic tangent as the activation function. Numerical results confirm that the deep parametric PDE method performs well in high-dimensional settings by presenting in a risk management problem of high interest for the financial industry.

Keywords: Deep neural networks; Deep parametric PDE method; DNN approximation theory; DNN expression rates; High-dimensional partial differential equations; Option pricing; Exposure calculation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-023-05315-4

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