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

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  • Kathrin Glau

    (Queen Mary University of London)

  • Linus Wunderlich

    (Queen Mary University of London)

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.

Suggested Citation

  • Kathrin Glau & Linus Wunderlich, 2024. "Neural network expression rates and applications of the deep parametric PDE method in counterparty credit risk," Annals of Operations Research, Springer, vol. 336(1), pages 331-357, May.
    • Handle: RePEc:spr:annopr:v:336:y:2024:i:1:d:10.1007_s10479-023-05315-4
    DOI: 10.1007/s10479-023-05315-4
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    References listed on IDEAS

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