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Trapping the Ultimate Success

Author

Listed:
  • Alexander Gnedin

    (School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK)

  • Zakaria Derbazi

    (School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK)

Abstract

We introduce a betting game where the gambler aims to guess the last success epoch in a series of inhomogeneous Bernoulli trials paced randomly in time. At a given stage, the gambler may bet on either the event that no further successes occur, or the event that exactly one success is yet to occur, or may choose any proper range of future times (a trap). When a trap is chosen, the gambler wins if the last success epoch is the only one that falls in the trap. The game is closely related to the sequential decision problem of maximising the probability of stopping on the last success. We use this connection to analyse the best-choice problem with random arrivals generated by a Pólya-Lundberg process.

Suggested Citation

  • Alexander Gnedin & Zakaria Derbazi, 2022. "Trapping the Ultimate Success," Mathematics, MDPI, vol. 10(1), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:1:p:158-:d:718112
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    References listed on IDEAS

    as
    1. Mitsushi Tamaki & Qi Wang, 2010. "A Random Arrival Time Best-Choice Problem with Uniform Prior on the Number of Arrivals," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & Ider Tseveendorj (ed.), Optimization and Optimal Control, pages 499-510, Springer.
    2. T. J. Stewart, 1981. "The Secretary Problem with an Unknown Number of Options," Operations Research, INFORMS, vol. 29(1), pages 130-145, February.
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    Cited by:

    1. Emanuele Dolera, 2022. "Preface to the Special Issue on “Bayesian Predictive Inference and Related Asymptotics—Festschrift for Eugenio Regazzini’s 75th Birthday”," Mathematics, MDPI, vol. 10(15), pages 1-4, July.

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