Optimal stopping is a decision-making problem in probability theory and statistics, where one must decide the best time to take a particular action in order to maximize an expected reward or minimize a cost. The key challenge in optimal stopping is that the decision-maker often does not know the future values of the processes involved, making it necessary to make choices based on partial information.
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Choosing a stopping time to maximize an expected reward. For an adapted integrable reward process over a finite discrete horizon, the Snell envelope computes the conditional optimal reward by comparing immediate exercise with continuation.