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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.

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