On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights
Touzi, Nizar; Manolarakis, Konstantinos; Crisan, Dan (2010), On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights, Stochastic Processes and their Applications, 120, 7, p. 1133-1158. http://dx.doi.org/10.1016/j.spa.2010.03.015
TypeArticle accepté pour publication ou publié
Journal nameStochastic Processes and their Applications
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Abstract (EN)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 , 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.
Subjects / KeywordsMalliavin calculus; Monte Carlo methods; Weak approximations; BDEs
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Fournié, Eric; Lasry, Jean-Michel; Lebuchoux, Jérôme; Lions, Pierre-Louis; Touzi, Nizar (1999) Article accepté pour publication ou publié
Henry-Labordère, Pierre; Oudjane, Nadia; Tan, Xiaolu; Touzi, Nizar; Warin, Xavier (2017) Document de travail / Working paper