Threshold Rules for the Classical Prophet Inequality
This provides a cleaner proof technique for known results in optimal stopping theory, but is incremental for researchers in prophet inequalities.
The paper presents a unified threshold/surplus decomposition for single-threshold stopping rules in the classical prophet inequality, certifying deterministic thresholds (median, half-mean, balanced-surplus) and an averaged certificate for randomized thresholds. The result is a simplified analysis of known thresholds.
This note records a common threshold/surplus decomposition for single-threshold stopping rules in the classical prophet inequality. The same decomposition is used to certify several deterministic thresholds, including the median, half-mean, and balanced-surplus thresholds, and to give an averaged certificate for randomized thresholds distributed as the maximum.