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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

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Type
Article accepté pour publication ou publié
Date
2010
Journal name
Stochastic Processes and their Applications
Volume
120
Number
7
Publisher
Elsevier
Pages
1133-1158
Publication identifier
http://dx.doi.org/10.1016/j.spa.2010.03.015
Metadata
Show full item record
Author(s)
Touzi, Nizar
Manolarakis, Konstantinos
Crisan, Dan
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) [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.
Subjects / Keywords
Malliavin calculus; Monte Carlo methods; Weak approximations; BDEs
JEL
C15 - Statistical Simulation Methods: General

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