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arXiv · 2608.24552

Asymptotic Rounding Laws for Optimal Thresholds in Secretary Problems

Raúl Sánchez Galán
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Abstract

We study second-order asymptotics for optimal thresholds in secretary-type problems. Under a unimodality assumption and a local affine expansion of the discrete payoff increments, we establish a general principle showing that sufficiently accurate rational approximations to the leading threshold proportion yield exact optimal integer thresholds. Continued-fraction convergents provide an immediate application. We also derive an asymptotic rounding law and apply the results to several variants of the secretary problem with fixed and random horizons.

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Raúl Sánchez Galán. 2026-08-25. Asymptotic Rounding Laws for Optimal Thresholds in Secretary Problems. https://arxiv.org/abs/2608.24552

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