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Neural network approximation for superhedging prices

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  • Francesca Biagini
  • Lukas Gonon
  • Thomas Reitsam

Abstract

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 t>0$t>0$, 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.

Suggested Citation

  • Francesca Biagini & Lukas Gonon & Thomas Reitsam, 2023. "Neural network approximation for superhedging prices," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 146-184, January.
    • Handle: RePEc:bla:mathfi:v:33:y:2023:i:1:p:146-184
    DOI: 10.1111/mafi.12363
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    References listed on IDEAS

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    Cited by:

    1. Donatien Hainaut & Alex Casas, 2024. "Option pricing in the Heston model with physics inspired neural networks," Annals of Finance, Springer, vol. 20(3), pages 353-376, September.
    2. Hainaut, Donatien & Casas, Alex, 2024. "Option pricing in the Heston model with Physics inspired neural networks," LIDAM Discussion Papers ISBA 2024002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Lukas Gonon & Thilo Meyer-Brandis & Niklas Weber, 2024. "Computing Systemic Risk Measures with Graph Neural Networks," Papers 2410.07222, arXiv.org.

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