A New Method for Computing Asymptotic Results in Optimal Stopping Problems

Bayón, L.; Ayuso, Pedro Fortuny; Grau, J. M.; Oller-Marcén, Antonio M.; Ruiz, M. M.

doi:10.1007/s40840-022-01436-4

Cited by 1 publication

(1 citation statement)

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“…The techniques in our previous paper, which are extended in this study, employ the asymptotic analysis of difference and differential equations in order to establish and solve asymptotic differential equations for the quantities of interest. Differential equations were also used in [18,19]. In this study, we extend some of our results in [1] to the multiple stopping case through some inductive arguments and verify these results with simulations.…”

Section: Introductionsupporting

confidence: 66%

Asymptotic Duration for Optimal Multiple Stopping Problems

Entwistle,

Lustri,

Sofronov

2024

Mathematics

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We study the asymptotic duration of optimal stopping problems involving a sequence of independent random variables that are drawn from a known continuous distribution. These variables are observed as a sequence, where no recall of previous observations is permitted, and the objective is to form an optimal strategy to maximise the expected reward. In our previous work, we presented a methodology, borrowing techniques from applied mathematics, for obtaining asymptotic expressions for the expectation duration of the optimal stopping time where one stop is permitted. In this study, we generalise further to the case where more than one stop is permitted, with an updated objective function of maximising the expected sum of the variables chosen. We formulate a complete generalisation for an exponential family as well as the uniform distribution by utilising an inductive approach in the formulation of the stopping rule. Explicit examples are shown for common probability functions as well as simulations to verify the asymptotic calculations.

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Section: Introductionsupporting

confidence: 66%