Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/287822 
Year of Publication: 
2022
Citation: 
[Journal:] Mathematical Finance [ISSN:] 1467-9965 [Volume:] 33 [Issue:] 1 [Publisher:] Wiley [Place:] Hoboken, NJ [Year:] 2022 [Pages:] 146-184
Publisher: 
Wiley, Hoboken, NJ
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$t>0$, 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.
Subjects: 
deep learning
quantile hedging
superhedging
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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