Neural network approximation for superhedging prices

2021/07/29 by Biagini, Francesca, Gonon, Lukas, Reitsam, Thomas · 1 citation
#60H30 #91G15 #91G20 #FOS: Economics and business #Mathematical Finance (q-fin.MF)

paper · doi:10.48550/arxiv.2107.14113

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, 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.

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