英文标题：
《Multilevel path simulation for weak approximation schemes》
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作者：
Denis Belomestny, Tigran Nagapetyan
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最新提交年份：
2014
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英文摘要：
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify this general idea in the case of weak Euler scheme for L\\\'evy driven stochastic differential equations, and show that, given a weak convergence of order $\\alpha\\geq 1/2,$ the complexity of the corresponding \"weak\" MLMC estimate is of order $\\varepsilon^{-2}\\log ^{2}(\\varepsilon).$ The numerical performance of the new \"weak\" MLMC method is illustrated by several numerical examples.
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中文摘要：
本文讨论了用多层蒙特卡罗（MLMC）方法求解弱近似格式的可能性。结果表明，通过连续时间离散化级别之间的简单耦合，可以获得与强收敛情况下相同的复杂性增益。我们举例说明了这一一般思想在L掼evy驱动的随机微分方程的弱Euler格式的情况下，并表明，给定$\\alpha\\geq 1/2阶的弱收敛，相应的“弱”MLMC估计的复杂度为$\\varepsilon^{-2}\\log^{2}（\\varepsilon）通过几个数值例子说明了新的“弱”MLMC方法的数值性能。
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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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