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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. 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).

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