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

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) / Euler-type scheme / time discretization / first-order / error estimate

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