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- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022
- ISSN
- 1387-2834
- eISSN
- 1573-6946
- DOI
- 10.1007/s10690-022-09374-8
- Publisher site
- See Article on Publisher Site
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.
Journal
Asia-Pacific Financial Markets – Springer Journals
Published: Jun 1, 2023
Keywords: Asymptotic expansion; Backward stochastic differential equation; Control variate method; Deep BSDE solver; Deep learning; Weak approximation