An acceleration scheme for deep learning-based BSDE solver using weak expansions

Riu Naito and Toshihiro Yamada
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Riu Naito: Asset Management One Co., Ltd., Chiyoda-ku, Tokyo, Japan
Toshihiro Yamada: #x2020;Graduate School of Economics, Hitotsubashi University, Tokyo, Japan

International Journal of Financial Engineering (IJFE), 2020, vol. 07, issue 02, 1-12

Abstract: This paper gives an acceleration scheme for deep backward stochastic differential equation (BSDE) solver, a deep learning method for solving BSDEs introduced in Weinan et al. [Weinan, E, J Han and A Jentzen (2017). Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations, Communications in Mathematics and Statistics, 5(4), 349–380]. The solutions of nonlinear partial differential equations are quickly estimated using technique of weak approximation even if the dimension is high. In particular, the loss function and the relative error for the target solution become sufficiently small through a smaller number of iteration steps in the new deep BSDE solver.

Keywords: Deep learning; backward stochastic differential equations; nonlinear partial differential equations; weak approximation (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S2424786320500127

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