Moving Boundary Methods for Stochastic Control Problems

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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.