Adapted $θ$-Scheme and Its Error Estimates for Backward Stochastic Differential Equations

Abstract

In this paper we propose a new kind of high order numerical scheme for backward stochastic differential equations(BSDEs). Unlike the traditional $θ$-scheme, we reduce truncation errors by taking $θ$ carefully for every subinterval according to the characteristics of integrands. We give error estimates of this nonlinear scheme and verify the order of scheme through a typical numerical experiment.