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: Faculty of Economics, The University of Tokyo
Akihiko Takahashi: Faculty of Economics, The University of Tokyo
Masayuki Takahashi: Graduate School of Economics, The University of Tokyo

No CIRJE-F-1069, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: We demonstrate that the use of asymptotic expansion as prior knowledge in th e"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.

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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