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

Masaaki Fujii, Akihiko Takahashi and Masayuki Takahashi
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Masaaki Fujii: Quantitative Finance Course, Graduate School of Economics, The University of Tokyo
Akihiko Takahashi: Quantitative Finance Course, Graduate School of Economics, The University of Tokyo
Masayuki Takahashi: Quantitative Finance Course, Graduate School of Economics, The University of Tokyo

No CARF-F-423, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

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.

Pages: 17 pages
Date: 2017-10
New Economics Papers: this item is included in nep-big
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Citations: View citations in EconPapers (10)

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