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Exact tail asymptotics of the supremum attained by a Lévy process

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  • Asghari, N.M.
  • Dȩbicki, K.
  • Mandjes, M.

Abstract

In this short communication we analyze the tail asymptotics corresponding to the maximum value attained by a Lévy process with negative drift. The note has two contributions: a short and elementary proof of these asymptotics, and an importance sampling algorithm to estimate the rare-event probabilities under consideration.

Suggested Citation

  • Asghari, N.M. & Dȩbicki, K. & Mandjes, M., 2015. "Exact tail asymptotics of the supremum attained by a Lévy process," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 180-184.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:180-184
    DOI: 10.1016/j.spl.2014.09.005
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    References listed on IDEAS

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    1. Bertoin, J. & Doney, R. A., 1994. "Cramer's estimate for Lévy processes," Statistics & Probability Letters, Elsevier, vol. 21(5), pages 363-365, December.
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