On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights
On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights
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DOI：
10.1016/j.spa.2010.03.015
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发表时间：
2010-07
影响因子：
1.4
通讯作者：
D. Crisan;K. Manolarakis;N. Touzi
中科院分区：
文献类型：
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作者：
D. Crisan;K. Manolarakis;N. Touzi
我们提出了一个通用框架来分析后向 SDE 的蒙特卡洛模拟方案。一般结果用于重新审视 Bouchard 和 Touzi (2004) [6] 建议的算法的收敛性。通过在 [6] 中的 Malliavin 分部积分所产生的 Skorohod 积分展开式中保留高阶项，我们引入了后一种算法的变体，该变体可以显着降低数值复杂性。我们证明了这种改进的基于 Malliavin 的算法的收敛性，并得出了诱导误差的界限。特别是，我们表明，我们的简化所付出的代价是使用更准确的本地化函数。
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.