  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 $t>0$, 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.
