Mathematical Sciences: Abstract Gambling Theory, Stochastic Games, and Statistics

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The principal investigator will work on a number of problems in abstract gambling theory, which is a particular formulation of stochastic control, and on related problems in the theory of two- person, zero-sum stochastic games. Some of the research will treat fundamental questions about the optimal reward function in gambling and the value function in stochastic games. One of these questions for a general class of stochastic games is the existence of the value. Some of the research will also treat specific stochastic control problems and stochastic games. Finally research is also proposed on certain questions which arise in the theory of Bayesian statistics. The principal investigator will work on fundamental questions about optimal decision making through time in the presence of uncertainty. Abstract gambling theory treats problems in which a single decision maker needs to control a process so as to attain some well-defined objective. In stochastic games two players have opposing interests and each seeks to control the same process but toward opposite ends. The mathematical details of such problems can be highly technical, but solutions are of interest in many areas including economics, operations research, and finance.