Solving Backward Stochastic Differential Equations by Connecting the Short-term Expansions
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. We provide numerical examples of quadratic-growth (qg) BSDEs as well as standard Lipschitz BSDEs to illustrate the proposed scheme and its empirical convergence rate.