A Numerical Method and Its Error Estimates for the Decoupled Forward-Backward Stochastic Differential Equations (Communications in Computational Physics, 2014)
In this paper, a new numerical method for solving the decoupled forward-backward stochastic differential equations (FBSDEs) is proposed based on some specially derived reference equations. We rigorously analyze errors of the proposed methodunder general situations. Then we present error estimates for each of the specific caseswhen some classical numerical schemes for solving the forward SDE are taken in themethod; in particular, we prove that the proposed method is second-order accurateif used together with the order-2.0 weak Taylor scheme for the SDE. Some examplesare also given to numerically demonstrate the accuracy of the proposed method andverify the theoretical results.