From Ruf and Wang 2020

*The Stone-Weierstrass theorem asserts that any continuous function on a compact set can be approximated*

*by polynomials. Similarly, the universal approximation theorems ensure that ANNs approximate*

*continuous functions in a suitable way. In particular, ANNs are able to capture nonlinear dependencies*

*between input and output.*

*With this understanding, an ANN can be used for many applications related to option pricing and hedging.*

*In the most common form, an ANN learns the price of an option as a function of the underlying*

*price, strike price, and possibly other relevant option characteristics. Similarly, ANNs might also be trained*

*to learn implied*

Sure; *it is not even wrong.*

This is really fun, as I do experience almost on a daily basis the same answers, again and again, concerning the UAT and Weierstrass. Another one that is quite nice : kernels methods can't scale to industrial problems because they are quadratics in term of training set size.

Even if you prove that UAT / Weirestrass is useless here, or if you show that kernels methods are linears in term of training set size, they will stick to their holy hand grenad of Antioch. Their best members wrote

that deep learning provide non converging methods, or we show to them that deep learning does not work for partial differential equations ? Don't bother, it is more fun to share awards, to give kudos, and to waste private and public money.