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A New Method for Computing Asymptotic Results in Optimal Stopping Problems

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Abstract

In this paper, we present a novel method for computing the asymptotic values of both the optimal threshold and the probability of success in sequences of optimal stopping problems. This method, based on the resolution of a first-order linear differential equation, makes it possible to systematically obtain these values in many situations. As an example, we address nine variants of the well-known secretary problem, including the classical one, that appear in the literature on the subject, as well as four other unpublished ones.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Oviedo, Avda. Calvo Sotelo s/n, 33007, Oviedo, Spain

    L. Bayón, P. Fortuny Ayuso, J. M. Grau & M. M. Ruiz

  2. Centro Universitario de la Defensa de Zaragoza - IUMA, Ctra. Huesca s/n, 50090, Zaragoza, Spain

    A. M. Oller-Marcén

Authors
  1. L. Bayón
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  2. P. Fortuny Ayuso
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  3. J. M. Grau
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  4. A. M. Oller-Marcén
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  5. M. M. Ruiz
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Correspondence to A. M. Oller-Marcén.

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Communicated by Rosihan M. Ali.

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Bayón, L., Fortuny Ayuso, P., Grau, J.M. et al. A New Method for Computing Asymptotic Results in Optimal Stopping Problems. Bull. Malays. Math. Sci. Soc. 46, 46 (2023). https://doi.org/10.1007/s40840-022-01436-4

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  • DOI: https://doi.org/10.1007/s40840-022-01436-4

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