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A General ‘Bang-Bang’ Principle for Predicting the Maximum of a Random Walk
Let ( B t ) 0≤ t ≤ T be either a Bernoulli random walk or a Brownian motion with drift, and let M t := max{ B s : 0 ≤ s ≤ t }, 0 ≤ t ≤ T . In this paper we solve the general optimal …