Moving Boundary Methods for Stochastic Control Problems

随机控制问题的移动边界方法

• 批准号: 1100710
• 负责人: Kumar Muthuraman
• 金额: $ 20万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-05-01 至 2015-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1100710&HistoricalAwards=false
• 关键词: Moving; Boundary; Methods; Stochastic; Control

The research objective of this award is to develop and extend an emerging class of techniques referred to as Moving Boundary Methods for solving hard free-boundary problems in stochastic control. Stochastic control refers to optimal decision making under uncertainty. Applications can be found in a variety of physical, economic, management and biological systems. Despite their wide applicability, problems in these classes are not analytically tractable except in very special cases and several remain unsolved even numerically. This award specifically identifies some problems in financial engineering, operations management and healthcare. Each of these problems, while being very significant by itself, also has distinct features that will make the methods developed, applicable to larger classes of problems. If successful, the developed methods will solve a large class of decision-making problems previously considered intractable. The project brings together a set of very important and hard control problems under the unifying framework of free-boundary problems and seeks to develop a set of novel computational methods. Success in the project has two major implications. First, it significantly advances the research on stochastic control. Second, the results and insights gained in each of the four specific projects will have a direct impact in financial engineering, operations management and healthcare. Optimal decision-making in healthcare is in its infancy and is poised to have a huge impact in prolonging life expectancies and reducing costs. Success in this project will also give healthcare professionals the much-needed confidence to view more problems from a quantitative perspective.

该奖项的研究目标是开发和扩展一类新兴技术，称为移动边界方法，用于解决随机控制中的硬自由边界问题。随机控制是指在不确定性下做出最优决策。应用可以在各种物理、经济、管理和生物系统中找到。尽管它们具有广泛的适用性，但除了非常特殊的情况外，这些类别的问题在分析上是不易处理的，并且有一些问题甚至在数值上仍然无法解决。该奖项特别指出了金融工程、运营管理和医疗保健领域的一些问题。这些问题中的每一个虽然本身都非常重要，但也具有独特的特征，这些特征将使所开发的方法适用于更大类别的问题。如果成功，所开发的方法将解决一大类以前被认为棘手的决策问题。该项目在自由边界问题的统一框架下汇集了一组非常重要且难控制的问题，并寻求开发一套新颖的计算方法。该项目的成功有两个主要意义。首先，它显着推进了随机控制的研究。其次，四个具体项目中每一个项目所获得的结果和见解都将对金融工程、运营管理和医疗保健产生直接影响。医疗保健领域的最佳决策尚处于起步阶段，有望对延长预期寿命和降低成本产生巨大影响。该项目的成功还将给医疗保健专业人员带来急需的信心，让他们从定量的角度看待更多问题。