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arXiv · 1711.08857

Oscillation criteria for stopping near the top of a random walk

José A. Islas
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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 \cite{Allaart} 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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José A. Islas. 2017-11-24. Oscillation criteria for stopping near the top of a random walk. https://arxiv.org/abs/1711.08857

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