Neural network approximation for superhedging prices
Abstract
This article examines neural networkbased 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 networkbased price. This provides a neural networkbased 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.14113
 Bibcode:
 2021arXiv210714113B
 Keywords:

 Quantitative Finance  Mathematical Finance;
 91G15;
 91G20;
 60H30