On the inefficiency of state-independent importance sampling in the presence of heavy tails

Achal Bassamboo, Sandeep Juneja, Assaf Zeevi

Research output: Contribution to journalArticlepeer-review

Abstract

This paper proves that there does not exist an asymptotically optimal state-independent change-of-measure for estimating the probability that a random walk with heavy-tailed increments exceeds a "high" threshold before going below zero. Explicit bounds are given on the best asymptotic variance reduction that can be achieved by state-independent schemes.

Original languageEnglish
Pages (from-to)251-260
Number of pages10
JournalOperations Research Letters
Volume35
Issue number2
DOIs
StatePublished - Mar 2007
Externally publishedYes

Keywords

  • Asymptotic analysis
  • Heavy tails
  • Importance sampling
  • State-dependent change-of-measure

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