A Multistep Scheme for Decoupled Forward-Backward Stochastic Differential Equations. Issue 2 (24th May 2016)

• Record Type: Journal Article
• Authors: Zhao, Weidong; Zhang, Wei; Ju, Lili
• Is Part Of: Numerical mathematics. Volume 9:Issue 2(2016)
• Page Start: 262
• Page End: 288
• Publication Date: 2016-05-24
• Subjects: 60H35, -- 65C20, -- 60H10; Decoupled forward-backward stochastic differential equations, -- backward orthogonal polynomials, -- multi-step numerical scheme, -- error estimate, -- numerical analysis; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2016.m1421
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: Upon a set of backward orthogonal polynomials, we propose a novel multi-step numerical scheme for solving the decoupled forward-backward stochastic differential equations (FBSDEs). Under Lipschtiz conditions on the coefficients of the FBSDEs, we first get a general error estimate result which implies zero-stability of the proposed scheme, and then we further prove that the convergence rate of the scheme can be of high order for Markovian FBSDEs. Some numerical experiments are presented to demonstrate the accuracy of the proposed multi-step scheme and to numerically verify the theoretical results.