High order one-step methods for backward stochastic differential equations via Itô-Taylor expansion

In this work, by combining the Feynman-Kac formula with an Ito-Taylor expansion, we propose a class of high order one-step schemes for backward stochastic differential equations, which can achieve at most six order rate of convergence and only need the terminal conditions on the last one step. Numerical experiments are carried out to show the efficiency and high order accuracy of the proposed schemes.