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

Touzi, Nizar; Manolarakis, Konstantinos; Crisan, Dan

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

Publisher

Elsevier

Pages

1133-1158

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