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: The University of Tokyo
Akihiko Takahashi: The University of Tokyo
Masayuki Takahashi: The University of Tokyo

Asia-Pacific Financial Markets, 2019, vol. 26, issue 3, No 6, 408 pages

Abstract: 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 et al. (Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations, 2017b. arXiv:1706.04702 ), 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.

Keywords: Deep learning; BSDEs; Asymptotic expansion; Deep BSDE solver; FVA; American option; High dimensional BSDEs; Different lending; Borrowing rates (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (34)

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DOI: 10.1007/s10690-019-09271-7

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