Moving Boundary Methods for Stochastic Control Problems

该奖项的研究目标是开发和推广一种被称为移动边界方法的新兴技术，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条件下的最优决策。可以在各种物理、经济、管理和生物系统中找到应用。尽管它们具有广泛的适用性，但除了在非常特殊的情况下，这些类中的问题在分析上是不容易处理的，甚至有几个问题甚至在数值上仍然没有解决。该奖项特别指出了金融工程、运营管理和医疗保健方面的一些问题。这些问题中的每一个，虽然本身都很重要，但也有不同的特点，将使所开发的方法适用于更大类别的问题。如果成功，开发的方法将解决一大类以前被认为难以解决的决策问题。该项目将一系列非常重要和困难的控制问题集中在自由边界问题的统一框架下，并试图开发一套新的计算方法。该项目的成功有两个主要影响。首先，它极大地推动了随机控制的研究。其次，四个具体项目中每一个项目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。医疗保健的最佳决策还处于初级阶段，有望在延长预期寿命和降低成本方面产生巨大影响。这个项目的成功还将给医疗保健专业人员带来亟需的信心，从量化的角度看待更多问题。

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.