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Exit identities for Lévy processes observed at Poisson arrival times

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Exit identities for Lévy processes observed at Poisson arrival times. / Albrecher, Hansjörg; Ivanovs, Jevgenijs; Zhou, Xiaowen.

In: Bernoulli, Vol. 22, No. 3, 2016, p. 1364-1382.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

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Author

Albrecher, Hansjörg ; Ivanovs, Jevgenijs ; Zhou, Xiaowen. / Exit identities for Lévy processes observed at Poisson arrival times. In: Bernoulli. 2016 ; Vol. 22, No. 3. pp. 1364-1382.

Bibtex

@article{84e3a4a78cdf4772a175cf7c89f0dfce,
title = "Exit identities for L{\'e}vy processes observed at Poisson arrival times",
abstract = "For a spectrally one-sided L{\'e}vy process, we extend various two-sided exit identities to the situation when the process is only observed at arrival epochs of an independent Poisson process. In addition, we consider exit problems of this type for processes reflected either from above or from below. The resulting Laplace transforms of the main quantities of interest are in terms of scale functions and turn out to be simple analogues of the classical formulas.",
keywords = "Cram{\'e}r-Lundberg risk model, Dividends, Exit problem, Reflection, Spectrally negative Levy process",
author = "Hansj{\"o}rg Albrecher and Jevgenijs Ivanovs and Xiaowen Zhou",
year = "2016",
doi = "10.3150/15-BEJ695",
language = "English",
volume = "22",
pages = "1364--1382",
journal = "Bernoulli",
issn = "1350-7265",
publisher = "International Statistical Institute",
number = "3",

}

RIS

TY - JOUR

T1 - Exit identities for Lévy processes observed at Poisson arrival times

AU - Albrecher, Hansjörg

AU - Ivanovs, Jevgenijs

AU - Zhou, Xiaowen

PY - 2016

Y1 - 2016

N2 - For a spectrally one-sided Lévy process, we extend various two-sided exit identities to the situation when the process is only observed at arrival epochs of an independent Poisson process. In addition, we consider exit problems of this type for processes reflected either from above or from below. The resulting Laplace transforms of the main quantities of interest are in terms of scale functions and turn out to be simple analogues of the classical formulas.

AB - For a spectrally one-sided Lévy process, we extend various two-sided exit identities to the situation when the process is only observed at arrival epochs of an independent Poisson process. In addition, we consider exit problems of this type for processes reflected either from above or from below. The resulting Laplace transforms of the main quantities of interest are in terms of scale functions and turn out to be simple analogues of the classical formulas.

KW - Cramér-Lundberg risk model

KW - Dividends

KW - Exit problem

KW - Reflection

KW - Spectrally negative Levy process

UR - http://www.scopus.com/inward/record.url?scp=84964484523&partnerID=8YFLogxK

U2 - 10.3150/15-BEJ695

DO - 10.3150/15-BEJ695

M3 - Journal article

AN - SCOPUS:84964484523

VL - 22

SP - 1364

EP - 1382

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

IS - 3

ER -