Neural network approximation for superhedging prices

Artikel

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Mathematical Finance ; ISSN: 1467-9965 ; Volume: 33 ; Year: 2022 ; Issue: 1 ; Pages: 146-184 ; Hoboken, NJ: Wiley

Classification and Topics

• Subject: deep learning ; quantile hedging ; superhedging

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Biagini, Francesca ; Gonon, Lukas ; Reitsam, Thomas
• Event: Veröffentlichung
• (who): Wiley
• (where): Hoboken, NJ
• (when): 2022

Further information

• DOI: doi:10.1111/mafi.12363
• Last update: 10.03.2025, 11:43 AM CET