Mathematical Sciences: Topics in Stochastic Control and Diffusion Processes

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In stochastic control problems, a random phenomenon is observed which is to be controlled using knowledge of the probabalistic law that the phenomenon obeys and the past history of the observations. The goal is to minimize the expected value of an associated cost function. Although the dynamic propramming principle will in theory yield an optimal strategy, in practice the theoretical results rarely provide explicitly computable answers. One of the main objects of this research is to determine, as explicitly as possible, the form of optimal policies in specific stochastic control problems arising from consumption/investment issues. Other research will deal with the connections between optimal stopping problems and singular stochastic control. The latter involves control actions having singular parts. Of particular interest are so-called 'finite fuel' constraints wherein the amount of effort (fuel) available to the controller is limited.