  We demonstrate that the use of asymptotic expansion as prior knowledge in the
"deep BSDE solver", which is a deep learning method for high dimensional BSDEs
proposed by Weinan E, Han & Jentzen (2017), drastically reduces the loss
function and accelerates the speed of convergence. We illustrate the technique
and its implications by using Bergman's model with different lending and
borrowing rates as a typical model for FVA as well as a class of solvable BSDEs
with quadratic growth drivers. We also present an extension of the deep BSDE
solver for reflected BSDEs representing American option prices.
