Neural network approximation for superhedging prices

Biagini, Francesca ; Gonon, Lukas und Reitsam, Thomas (2022): Neural network approximation for superhedging prices. In: Mathematical Finance, Bd. 33, Nr. 1: S. 146-184

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 alpha-quantile hedging price converges to the superhedging price at time 0 for alpha tending to 1, and show that the alpha-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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0960-1627
• Sprache: Englisch
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 491502892