On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights

We propose a generic framework for the analysis of Monte Carlo simulation schemes of backward SDEs. The general results are used to re-visit the convergence of the algorithm suggested by Bouchard and Touzi (2004) [6]. By keeping the higher order terms in the expansion of the Skorohod integrals resulting from the Malliavin integration by parts in [6], we introduce a variant of the latter algorithm which allows for a significant reduction of the numerical complexity. We prove the convergence of this improved Malliavin-based algorithm, and derive a bound on the induced error. In particular, we show that the price to pay for our simplification is to use a more accurate localizing function.