An Explicit Second Order Scheme for Decoupled Anticipated Forward Backward Stochastic Differential Equations

Abstract

The Feynman-Kac formula and the Lagrange interpolation method are used in the construction of an explicit second order scheme for decoupled anticipated forward backward stochastic differential equations. The stability of the scheme is rigorously proved and error estimates are established. The scheme has the second order accuracy when weak order 2.0 Taylor scheme is employed to solve stochastic differential equations. Numerical tests confirm the theoretical findings.