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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.