An approximation result and Monte Carlo simulation of the adapted solution of the one-dimensional backward stochastic differential equation

In this paper, we give an approximation result for the adapted solution of the one-dimensional backward stochastic differential equation driven by a one-dimensional Brownian motion (BSDE for short). To prove our main result, we linearize the generator of the BSDE around a deterministic nominal reference trajectory by using a Taylor series expansion. We then find an approximate linear model of the BSDE. A test of our method is given with a numerical scheme driven by the Monte Carlo simulation. We believe that our result is new and valid for the multidimensional case.