Research

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

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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 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.
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