Neural network approximation for superhedging prices - Francesca Biagini; Lukas Gonon; Thomas Reitsam (Mathematical Finance, 2022)
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>0t>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.
Keywords: 519; deep learning; quantile hedging; superhedging