Numerical Algorithms for 1-d Backward Stochastic Differential Equations:   Convergence and Simulations
  In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs. 
Shige Peng and Mingyu Xu