Issues in high-dimensional quasi-monte carlo sampling

高维准蒙特卡罗采样中的问题

• 批准号: 238959-2010
• 负责人: Lemieux, Christiane
• 金额: $ 1.46万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508713
• 关键词: Issues; dimensional; quasi; monte; carlo

Suppose a financial analyst wants to price a complex product. The Monte Carlo method can be used for that purpose. It uses random sampling in order to "simulate" possible financial scenarios, and for each, the corresponding value of the product under study. By repeating this process several times, a sample of possible values for the product is created, which can then be used for inference, e.g., its mean gives an estimator for the product's price. Quasi-Monte Carlo methods aim at improving this final estimation phase by replacing the random sampling inherent in Monte Carlo by a more structured form of sampling. This improved sampling is based on the use of constructions that attempt to place points in a domain in a very uniform way. These methods have gained a lot of attention in the last 10 to 15 years, as they have proven to be useful on difficult high-dimensional problems in finance, e.g., involving the simulation of several financial assets over long periods of time. More precisely, they can provide estimators with a smaller error than those obtained by applying Monte Carlo, using the same amount of computational effort. Because of this success, these methods are now used in applications that are becoming increasingly complex.

假设一位金融分析师想要对一种复杂产品进行定价。蒙特卡洛方法可用于此目的。它使用随机抽样来“模拟”可能的金融场景，并为每个场景模拟所研究产品的相应价值。通过多次重复此过程，创建产品可能值的样本，然后可以将其用于推理，例如，其平均值给出产品价格的估计量。准蒙特卡罗方法旨在通过用更结构化的采样形式取代蒙特卡罗中固有的随机采样来改进最终估计阶段。这种改进的采样基于尝试以非常统一的方式将点放置在域中的结构的使用。这些方法在过去 10 到 15 年中受到了广泛关注，因为它们已被证明对于解决金融中的困难高维问题非常有用，例如涉及长时间模拟多种金融资产。更准确地说，在使用相同量的计算量的情况下，它们可以为估计器提供比应用蒙特卡罗获得的误差更小的误差。由于这一成功，这些方法现在被用于变得越来越复杂的应用中。