英文标题：
《Pricing American options using martingale bases》
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作者：
J\\\'er\\^ome Lelong
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最新提交年份：
2016
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英文摘要：
In this work, we propose an algorithm to price American options by directly solving the dual minimization problem introduced by Rogers. Our approach relies on approximating the set of uniformly square integrable martingales by a finite dimensional Wiener chaos expansion. Then, we use a sample average approximation technique to efficiently solve the optimization problem. Unlike all the regression based methods, our method can transparently deal with path dependent options without extra computations and a parallel implementation writes easily with very little communication and no centralized work. We test our approach on several multi--dimensional options with up to 40 assets and show the impressive scalability of the parallel implementation.
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中文摘要：
在这项工作中，我们提出了一个算法来定价美式期权直接解决双重最小化问题由罗杰斯介绍。我们的方法依赖于通过有限维维纳混沌展开来逼近一致平方可积鞅集。然后，我们使用样本平均近似技术来有效地解决优化问题。与所有基于回归的方法不同，我们的方法可以透明地处理路径相关的选项，而无需额外的计算，并且并行实现易于编写，只需很少的通信和集中的工作。我们在多达40个资产的几个多维选项上测试了我们的方法，并展示了并行实现令人印象深刻的可伸缩性。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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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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