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摘要翻译：
Giles（{\IT运筹学}，56(3):607-617，2008)提出的多级Monte Carlo路径模拟方法利用强收敛特性，将不同分辨率的模拟结合起来，提高了计算复杂度。本文分析了Milstein离散化方法的有效性；与标准的Euler-Maruyama方法相比，该方法具有较好的强收敛阶，并证明了该方法使多级估计方差的收敛阶得到了改进。数值结果也给出了篮子选项，以说明分析的相关性。
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英文标题：
《Analysis of multilevel Monte Carlo path simulation using the Milstein
discretisation》
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作者：
Michael B. Giles, Kristian Debrabant, Andreas R\"o{\ss}ler
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最新提交年份：
2019
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
The multilevel Monte Carlo path simulation method introduced by Giles ({\it Operations Research}, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. In this paper we analyse its efficiency when using the Milstein discretisation; this has an improved order of strong convergence compared to the standard Euler-Maruyama method, and it is proved that this leads to an improved order of convergence of the variance of the multilevel estimator. Numerical results are also given for basket options to illustrate the relevance of the analysis.
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PDF链接：
https://arxiv.org/pdf/1302.4676
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