Before revision: In this article , we propose a new numerical computation scheme for Markovian backward stochastic differential equations (BSDEs ) by connecting the semi-analytic short-term approximation applied to each time interval, which has a very simple form to implement. We give the error analysis for BSDEs which have generators of quadratic growth with respect to the control variables and bounded terminal conditions. Although the scheme requires higher regularities than the standard method , one can avoid altogether time-consuming Monte Carlo simulation or other numerical integration for estimating conditional expectations at each space-time node.
After revision: In this article , we propose a new numerical computation scheme for Markovian backward stochastic differential equations (BSDEs ) by connecting the semi-analytic asymptotic expansions applied to short-time intervals. Although there remains a condition which needs to be checked a posteriori , one can avoid altogether time-consuming Monte Carlo simulation or other numerical integration for estimating conditional expectations at each space-time node.