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

TL;DR

This paper introduces the use of asymptotic expansion as prior knowledge in the deep BSDE solver, significantly improving convergence speed and reducing loss in high-dimensional BSDEs, with applications to financial models.

Contribution

It presents a novel integration of asymptotic expansion into the deep BSDE solver, enhancing its efficiency and extending it to reflected BSDEs for American options.

Findings

Reduced loss function in high-dimensional BSDEs

Accelerated convergence speed of the deep BSDE solver

Extended method to reflected BSDEs for American options

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 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.