英文标题：
《An Introduction to Multilevel Monte Carlo for Option Valuation》
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作者：
Desmond J. Higham
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最新提交年份：
2015
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英文摘要：
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation. In 2008, Giles proposed a remarkable improvement to the approach of discretizing with a numerical method and applying standard Monte Carlo. His multilevel Monte Carlo method offers an order of speed up given by the inverse of epsilon, where epsilon is the required accuracy. So computations can run 100 times more quickly when two digits of accuracy are required. The multilevel philosophy has since been adopted by a range of researchers and a wealth of practically significant results has arisen, most of which have yet to make their way into the expository literature. In this work, we give a brief, accessible, introduction to multilevel Monte Carlo and summarize recent results applicable to the task of option evaluation.
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中文摘要：
蒙特卡罗是一种简单而灵活的工具，广泛应用于计算金融领域。在这种情况下，兴趣量通常是通过随机微分方程定义的随机变量的期望值。2008年，Giles提出了一个显著的改进方案，即使用数值方法和标准蒙特卡罗进行离散化。他的多级蒙特卡罗方法提供了一个由ε的倒数给出的加速顺序，其中ε是所需的精度。因此，当需要两位数的精度时，计算速度可以提高100倍。自那以后，多层次哲学被一系列研究人员采用，并产生了大量具有实际意义的结果，其中大多数尚未进入解释性文献。在这项工作中，我们简要介绍了多层蒙特卡罗，并总结了适用于期权评估任务的最新结果。
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分类信息：

一级分类：Mathematics 数学
二级分类：Numerical Analysis 数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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一级分类：Computer Science 计算机科学
二级分类：Computational Engineering, Finance, and Science 计算工程、金融和科学
分类描述：Covers applications of computer science to the mathematical modeling of complex systems in the fields of science, engineering, and finance. Papers here are interdisciplinary and applications-oriented, focusing on techniques and tools that enable challenging computational simulations to be performed, for which the use of supercomputers or distributed computing platforms is often required. Includes material in ACM Subject Classes J.2, J.3, and J.4 (economics).
涵盖了计算机科学在科学、工程和金融领域复杂系统的数学建模中的应用。这里的论文是跨学科和面向应用的，集中在技术和工具，使挑战性的计算模拟能够执行，其中往往需要使用超级计算机或分布式计算平台。包括ACM学科课程J.2、J.3和J.4（经济学）中的材料。
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一级分类：Physics 物理学
二级分类：Data Analysis, Statistics and Probability 数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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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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一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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