Discussion Papers 2017

CIRJE-F-1069	"Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High Dimensional BSDEs"
Author Name	Fujii, Masaaki, Akihiko Takahashi and Masayuki Takahashi
Date	October 2017
Full Paper	PDF file
Remarks	Revised in March 2019; forthcoming in Asia-Pacific Financial Markets.

Abstract
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 thespeed 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.
Keywords:

Abstract

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 thespeed 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.

Keywords: