Mathematical Sciences: Abstract Gambling Theory Bayesian Statistics and Probability

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Research is proposed in three related areas. The principal investigator has a long record of distinguished research in the area of abstract gambling theory. In this project he will investigate certain fundamental problems of both discrete and continuous gambling theory such as countably additive theory and measurability. Specific gambling problem to be considered is of minimizing the expected time to goal in a Bayesian framework. The second project will explore the relationship of coherent inference to the theory of admissible inference in Bayesian statistics and will develop a family of tractable priors with required properties. The last project deals with optimal stopping and its relation with abstract gambling theory.