Neural network approximation for superhedging prices

Francesca Biagini; Lukas Gonon; Thomas Reitsam

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arXiv · 2107.14113

Neural network approximation for superhedging prices

Francesca Biagini·Lukas Gonon·Thomas Reitsam

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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.

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BibTeX RIS

Francesca Biagini, Lukas Gonon, Thomas Reitsam. 2021-07-29. Neural network approximation for superhedging prices. https://arxiv.org/abs/2107.14113

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