WIAS Preprint No. 1774, (2013)

On non-asymptotic optimal stopping criteria in Monte Carlo simulations


  • Bayer, Christian
    ORCID: 0000-0002-9116-0039
  • Hoel, Håkon
  • von Schwerin, Erik
  • Tempone, Raúl

2010 Mathematics Subject Classification

  • 65C05 62L12 62L15


  • Monte Carlo methods, optimal stopping, sequential stopping rules, non-asymptotic




We consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. The performance of a typical second moment based sequential stopping rule MC method is shown to be unreliable in such settings both by numerical examples and through analysis. By analysis and approximations, we construct a higher moment based stopping rule which is shown in numerical examples to perform more reliably and only slightly less efficiently than the second moment based stopping rule.

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