Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs



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.