Abstract
Let X 1,…, X n be independent, identically distributed random variables that are nonnegative and integrable, with known continuous distribution. These random variables are observed sequentially, and the goal is to maximize the expected X value at which one stops. Let V n denote the optimal expected return of a player who can observe at time j only whether X j is a relative record (j = 1,…, n), and W n that of a player who observes at time j the actual value of X j . It is shown that V n > a n W n , where , and this inequality is sharp.
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Recommended by Nitis Mukhopadhyay