Euler-type schemes for weakly coupled forward-backward stochastic differential equations and optimal convergence analysis

doi:10.1007/s11464-014-0366-6

Front. Math. China

2015, Vol. 10

Issue (2) : 415-434 https://doi.org/10.1007/s11464-014-0366-6

RESEARCH ARTICLE

Euler-type schemes for weakly coupled forward-backward stochastic differential equations and optimal convergence analysis

Wei ZHANG,Weidong ZHAO(

)

School of Mathematics, Finance Institute, Shandong University, Jinan 250100, China

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Abstract

We introduce a new Euler-type scheme and its iterative algorithm for solving weakly coupled forward-backward stochastic differential equations (FBSDEs). Although the schemes share some common features with the ones proposed by C. Bender and J. Zhang [Ann. Appl. Probab., 2008, 18: 143–177], less computational work is needed for our method. For both our schemes and the ones proposed by Bender and Zhang, we rigorously obtain first-order error estimates, which improve the half-order error estimates of Bender and Zhang. Moreover, numerical tests are given to demonstrate the first-order accuracy of the schemes.

Keywords Weakly coupled forward-backward stochastic differential equations (FBSDEs) time discretization first-order error estimate Euler-type scheme

Corresponding Author(s): Weidong ZHAO

Issue Date: 12 February 2015

Cite this article:

Wei ZHANG,Weidong ZHAO. Euler-type schemes for weakly coupled forward-backward stochastic differential equations and optimal convergence analysis[J]. Front. Math. China, 2015, 10(2): 415-434.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0366-6
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I2/415

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