Advanced Computational Stochastic Dynamic Programming for Continuous Time Problems

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Hanson0207081 The principal investigator and his colleagues developcomputational stochastic dynamic programming methods to findapproximations to optimally control the expected objective valuefor a wide variety of applications. These applications includethe optimal treatment of cancer by chemotherapy drugs, theoptimal financial investment portfolio and parameter estimation,optimal control of stochastic manufacturing systems, and theoptimal remediation of ground water pollution. The wide scope oftestbed applications helps to increase the robustness of theiradvanced numerical methods by having to treat a variety of modelsand boundary conditions. Another characteristic of many of theseapplications is that the most severe changes happen as jumps ofthe system and many models utilize stochastic jump-diffusionprocesses. The computation of optimal approximations in jumpenvironments is a unique feature of the models, where increasedrealism of the models more than compensates for the added burdenof increased computational complexity over diffusions. Theinvestigator is writing an applied book with a colleague onstochastic processes and control emphasizing jump-diffusionmodels to give broader impact to their more general results. Themathematical level is intermediate so that it is accessible anduseful to those who actually work with real applications inscience, engineering, and finance. The principal investigator and colleagues study models ofsystems in uncertain environments and seek optimal computationalapproximations to get the best performance from these systems.Many of the applications are national challenges. Oneapplication is the optimal management of cancer chemotherapy whencancer cells develop resistance to a cancer drug combination.The impact of finding optimal cancer treatment schedules would besignificant because cancer is a leading cause of death. Anotherapplication is computational solutions for optimal investorportfolio and consumption problems in a market with crashes invalue; the benefit is a better understanding of our nation's andthe world's financial systems. A third application is theoptimal scheduling of manufacturing systems subject to uncertainfailures, repairs, and other disruptions. Here improvedefficiencies are important for the national economic well-being.A fourth application is the optimal remediation of pollution inground water, with important environmental consequences. Studentsare involved in these projects, providing them with significantexperience in interdisciplinary research. Finally, theinvestigators are writing an intermediate level applied book onthe optimal control of systems in uncertain environments withlarge changes, integrating their results over a wide variety ofapplications. The aim is to bring these ideas in a moreaccessible form to scientists and engineers.