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

D. Crisan, K. Manolarakis, N. Touzi

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1133-1158
Number of pages26
JournalStochastic Processes and their Applications
Issue number7
StatePublished - Jul 2010


  • BSDEs
  • Malliavin calculus
  • Monte Carlo methods
  • Weak approximations

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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