Exact tail asymptotics of the supremum attained by a Lévy process

N.M. Asghari; M.R.H. Mandjes; K.G. Debicki

doi:10.1016/j.spl.2014.09.005

Exact tail asymptotics of the supremum attained by a Lévy process

N.M. Asghari, M.R.H. Mandjes, K.G. Debicki

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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. Keywords: Lévy processes; Second factorization identity; Tail asymptotics; Importance sampling

Original language	English
Pages (from-to)	180-184
Journal	Statistics and Probability Letters
Volume	96
DOIs	https://doi.org/10.1016/j.spl.2014.09.005
Publication status	Published - 2015

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title = "Exact tail asymptotics of the supremum attained by a L{\'e}vy process",

abstract = "In this short communication we analyze the tail asymptotics corresponding to the maximum value attained by a L{\'e}vy 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. Keywords: L{\'e}vy processes; Second factorization identity; Tail asymptotics; Importance sampling",

author = "N.M. Asghari and M.R.H. Mandjes and K.G. Debicki",

year = "2015",

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AU - Asghari, N.M.

AU - Mandjes, M.R.H.

AU - Debicki, K.G.

PY - 2015

Y1 - 2015

N2 - 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. Keywords: Lévy processes; Second factorization identity; Tail asymptotics; Importance sampling

AB - 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. Keywords: Lévy processes; Second factorization identity; Tail asymptotics; Importance sampling

U2 - 10.1016/j.spl.2014.09.005

DO - 10.1016/j.spl.2014.09.005

M3 - Article

SN - 0167-7152

VL - 96

SP - 180

EP - 184

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

Exact tail asymptotics of the supremum attained by a Lévy process

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