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Neural network approximation for superhedging prices
Author(s) -
Biagini Francesca,
Go Lukas,
Reitsam Thomas
Publication year - 2023
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12363
Subject(s) - artificial neural network , infimum and supremum , econometrics , economics , computer science , mathematical economics , mathematics , artificial intelligence , mathematical analysis
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 fort > 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.