摘要翻译：
本文介绍了一种新的美式期权数值定价方法。其主要思想是（随机）选择有限个合适的超额函数，并在这些函数的跨度中寻找增益函数的最小优势。所得问题是一个线性半无限规划问题，可以用标准算法求解。这为原始问题带来了很好的上界。对于我们的算法，不需要空间和时间的离散化，也不需要仿真。此外，它甚至适用于高维问题。该算法不仅为一个起点提供了一个值的近似值，而且为延拓集上的完全值函数提供了一个值的近似值，从而可以计算出最优的运动区域，例如希腊人。我们将该算法应用于（一维和）多维扩散和L\'evy过程，证明了该算法的快速性和准确性。
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英文标题：
《A method for pricing American options using semi-infinite linear
  programming》
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作者：
S\"oren Christensen
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最新提交年份：
2011
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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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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：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
  We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these functions. The resulting problem is a linear semi-infinite programming problem, that can be solved using standard algorithms. This leads to good upper bounds for the original problem. For our algorithms no discretization of space and time and no simulation is necessary. Furthermore it is applicable even for high-dimensional problems. The algorithm provides an approximation of the value not only for one starting point, but for the complete value function on the continuation set, so that the optimal exercise region and e.g. the Greeks can be calculated. We apply the algorithm to (one- and) multidimensional diffusions and to L\'evy processes, and show it to be fast and accurate.
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PDF链接：
https://arxiv.org/pdf/1103.4483