A New Efficient Approximation Scheme for Solving High-Dimensional Semilinear PDEs: Control Variate Method for Deep BSDE Solver

Akihiko Takahashi, Yoshifumi Tsuchida and Toshihiro Yamada
Additional contact information
Akihiko Takahashi: Faculty of Economics, The University of Tokyo
Yoshifumi Tsuchida: Graduate School of Economnics, Faculty of Economics, Hitotsubashi University
Toshihiro Yamada: Graduate School of Economnics, Hitotsubashi University and Japan Science and Technology Agency (JST)

No CIRJE-F-1159, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This paper introduces a new approximation scheme for solving high-dimensional semilinear partial differential equations (PDEs) and backward stochastic differential equations (BSDEs). First, we decompose a target semilinear PDE (BSDE) into two parts, linear PDE part and non- linear PDE part. Then, we employ a Deep BSDE solver with a new control variate method to solve those PDEs, where approximations based on an asymptotic expansion technique are effectively applied to the linear part and also used as control variates for the nonlinear part. Moreover, our theoretical result indicates that errors of the proposed method become much smaller than those of the original Deep BSDE solver. Finally, we show numerical experiments to demonstrate the validity of our method, which is consistent with the theoretical result in this paper.

Pages: 49pages
Date: 2021-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.cirje.e.u-tokyo.ac.jp/research/dp/2021/2021cf1159.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2021cf1159

Access Statistics for this paper

More papers in CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo Contact information at EDIRC.
Bibliographic data for series maintained by CIRJE administrative office ().