Control Variate Method for Deep BSDE Solver Using Weak Approximation

Yoshifumi Tsuchida ()
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Yoshifumi Tsuchida: Asset Management One Co., Ltd.

Asia-Pacific Financial Markets, 2023, vol. 30, issue 2, No 1, 273-296

Abstract: Abstract The paper develops a new deep learning based scheme for solving high-dimensional nonlinear forward-backward stochastic differential equations (FBSDE) and associated partial differential equations. Firstly, the original BSDE is split into the linear dominant BSDE part and the nonlinear residual BSDE part. Then the linear BSDE part is approximated with high accuracy using a weak approximation technique. To approximate the nonlinear BSDE part, Deep BSDE solver is applied with asymptotic expansions which work as control variates. A sharp error estimate provides how the new scheme improves the original Deep BSDE method. Numerical experiments for high-dimensional nonlinear models show the validity and the effectiveness of the new scheme in financial application.

Keywords: Asymptotic expansion; Backward stochastic differential equation; Control variate method; Deep BSDE solver; Deep learning; Weak approximation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10690-022-09374-8

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