An Optimal Selection Problem Associated with the Poisson Process

DOI10.1137/1123066zbMath0426.62058OpenAlexW2071424358MaRDI QIDQ3862282

Zabczyk, Jerzy, Richard Cowan

Publication date: 1979

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/1123066

zbMATH Keywords

secretary problemoptimal selectionstationary Poisson process

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Stopping times; optimal stopping problems; gambling theory (60G40) Continuous-time Markov processes on discrete state spaces (60J27) Optimal stopping in statistics (62L15)

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The 1/e-strategy is sub-optimal for the problem of best choice under no information ⋮ A note on the full-information Poisson arrival selection problem ⋮ Explicit optimal value for Dynkin's stopping game ⋮ A full information pricing problem for the sale of several identical commodities ⋮ Embedding optimal selection problems in a Poisson process ⋮ A game version of the Cowan-Zabczyk-Bruss' problem ⋮ Optimal Shopping When the Sales Are on—a Markovian Full-Information Best-Choice Problem ⋮ An interactive method for the optimal selection problem with two decision makers ⋮ A loss minimization problem ⋮ The best choice problem with random arrivals: how to beat the \(1 / e\)-strategy ⋮ A version of the Elfving problem with random starting time

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