Oscillation criteria for stopping near the top of a random walk

2017/11/24 by José A. Islas, Islas, José A.
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1711.08857

arxiv created 2017/11/24 · arxiv updated 2017/11/27

Abstract

Consider the problem of maximizing the probability of stopping with one of the two highest values in a Bernoulli random walk with arbitrary parameter p and finite time horizon n. Allaart \citeAllaart proved that the optimal strategy is determined by an interesting sequence of constants \p_n\. He conjectured the asymptotic behavior to be 1/2. In this work the best lower bound for this sequence is found and more of its properties are proven towards solving the conjecture.

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