Novel multi-step predictor-corrector schemes for backward stochastic differential equations

Novel multi-step predictor-corrector numerical schemes have been derived for approximating decoupled forward-backward stochastic differential equations. The stability and high order rate of convergence of the proposed schemes are rigorously proved. We also present a sufficient and necessary condition for the stability of the schemes. Numerical experiments are given to illustrate the stability and convergence rates of the proposed methods.