Neural network approximation for superhedging prices

Biagini, Francesca ; Gonon, Lukas und Reitsam, Thomas (2022): Neural network approximation for superhedging prices. In: Mathematical Finance, Vol. 33, No. 1: pp. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0960-1627
• Language: English
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 491502892