Prophet and Minimax Problems in Optimal Stopping Theory

摘要

The thesis consists of two parts, namely prophet problems and minimax theorems in 'partial information' optimal stopping problems. Both parts are strongly related to the general theory of optimal stopping. Roughly speaking, this theory can be described in gambling terms as follows. A gambler is confronted with a sequence of games. At each stage, the gambler may choose to quit (stop) or to play the next game, basing his choice on the outcomes of the previous games, and perhaps, on some additional information. For a given sequence of games, it asks when should the gambler stop so as to maximize his expected return, and what is this expected return. These questions are answered in some special cases.