Neural network approximation for superhedging prices

Francesca Biagini, Lukas Gonon and Thomas Reitsam

Papers from arXiv.org

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 $t>0$, 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.

Date: 2021-07
New Economics Papers: this item is included in nep-big, nep-cmp, nep-isf and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2107.14113

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