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A Class of Efficient Multistep Methods for Forward Backward Stochastic Differential Equations

A Class of Efficient Multistep Methods for Forward Backward Stochastic Differential Equations

Year:    2024

Author:    Xiao Tang, Jie Xiong

Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 4 : pp. 904–932

Abstract

A class of efficient multistep methods for forward backward stochastic differential equations (FBSDEs) are proposed and studied in this paper. According to the characteristic of our multistep methods and replacing the corresponding Brownian motion increments with appropriate two-point distributed random variables, we obtain a very efficient algorithm to approximate the conditional expectations involved in the multistep methods. It is thanks to this efficient algorithm that we can obtain a class of efficient fully discrete form of high-order methods for the FBSDEs. Finally, some numerical results are presented to illustrate the efficiency of our multistep methods.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2024-0010

Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 4 : pp. 904–932

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:    Forward backward stochastic differential equations multistep methods efficient high-order methods conditional expectations.

Author Details

Xiao Tang

Jie Xiong