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  Bergman's model with different lending and borrowing rates , and a class of quadratic-growth BSDEs . We also present an extension of the deep BSDE solver for reflected BSDEs using an American basket option as an example .
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 .
A
using
R
, and a class of quadratic-growth BSDEs
as a typical model for FVA as well as a class of solvable BSDEs with quadratic growth drivers
R
using an American basket option as an example
representing American option prices