  The pricing of Bermudan options amounts to solving a dynamic programming
principle, in which the main difficulty, especially in high dimension, comes
from the conditional expectation involved in the computation of the
continuation value. These conditional expectations are classically computed by
regression techniques on a finite dimensional vector space. In this work, we
study neural networks approximations of conditional expectations. We prove the
convergence of the well-known Longstaff and Schwartz algorithm when the
standard least-square regression is replaced by a neural network approximation.
We illustrate the numerical efficiency of neural networks as an alternative to
standard regression methods for approximating conditional expectations on
several numerical examples.
