Mathematical Sciences: Optimal Stopping and Extremes in Discrete Parameter Stochastic Processes

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This project, described in gambling terminology, has a number of applications in dynamic programing, management science and economics. The game is given by a sequence of random variables denoting the payoff. A stop rule in practice has to be based on only the knowledge of the game up to the point. Such non-anticipatory, adaptive procedure is compared to the reward of the game if complete foresight was available. For selected stopping rules, the principal investigator plans to compare the sequences of payoffs and find sharp inequalities of various kinds. Some of the strategies used for optimizing the reward will take in to account the information in the observations as well as the information in the prior distributions.