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.
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