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

By D. Crisan, K. Manolarakis & N. Touzi (Cahier de la Chaire n°30)

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). By keeping the higher order terms in the expansion of the Skorohod integrals resulting from the Malliavin integration by parts in Bouchard and Touzi (2004), 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.

Keywords: BSDEs, Weak approximations, Monte Carlo methods, Malliavin calculus

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