A New Second-Order One-Step Scheme for Solving Decoupled FBSDES and Optimal Error Estimates

Authors

  • Yang Li State Key Laboratory for Modification of Chemical Fibers and Polymer Materials, College of Materials Science and Engineering, Donghua University, Shanghai 201620, China
  • Jie Yang School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, China.
  • Weidong Zhao School of Mathematics, Shandong University, Jinan, Shandong 250100, China

DOI:

https://doi.org/10.4208/eajam.280519.180919

Keywords:

FBSDEs, simplified weak Itô-Taylor scheme, second-order scheme, error estimate.

Abstract

A novel second-order numerical scheme for solving decoupled forward backward stochastic differential equations is proposed. Unlike known second-order schemes for such equations, the forward stochastic differential equations are approximated by a simplified weak order-2 Itô-Taylor scheme. This makes the method more implementable and enhances the accuracy. If the operators involved satisfy certain commutativity conditions, the scheme with quadratic convergence can be simplified, which is important in applications. The stability of the method is studied and second-order optimal error estimates are obtained.

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Published

2020-04-01

Issue

Vol. 10 No. 2 (2020)

Section

Articles