A factorization of a Lévy process over a phase-type horizon

Søren Asmussen; Jevgenijs Ivanovs

doi:10.1080/15326349.2018.1513335

A factorization of a Lévy process over a phase-type horizon

^*Corresponding author for this work

Department of Mathematics

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7 Citations (Scopus)

Abstract

This note provides a factorization of a Lévy pocess over a phase-type horizon τ given the phase at the supremum, thereby extending the Wiener–Hopf factorization for τ exponential. One of the factors is defined using time reversal of the phase process. It is shown that there are a variety of time-reversed representations, all yielding the same factor. Consequences of this are discussed and examples provided. Additionally, some explicit formulas for the joint law of the supremum and the terminal value of the process at τ are given.

Original language	English
Journal	Stochastic Models
Volume	34
Issue	4
Pages (from-to)	397-408
Number of pages	12
ISSN	1532-6349
DOIs	https://doi.org/10.1080/15326349.2018.1513335
Publication status	Published - 2018

Keywords

phase-type distribution
splitting
time reversal
Wiener–Hopf factorization
WIENER-HOPF FACTORIZATION
LAW
MARKOV-ADDITIVE PROCESSES
1ST PASSAGE
Wiener-Hopf factorization
POSITIVE JUMPS

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10.1080/15326349.2018.1513335

https://arxiv.org/pdf/1803.00273.pdf

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title = "A factorization of a L{\'e}vy process over a phase-type horizon",

abstract = "This note provides a factorization of a L{\'e}vy pocess over a phase-type horizon τ given the phase at the supremum, thereby extending the Wiener–Hopf factorization for τ exponential. One of the factors is defined using time reversal of the phase process. It is shown that there are a variety of time-reversed representations, all yielding the same factor. Consequences of this are discussed and examples provided. Additionally, some explicit formulas for the joint law of the supremum and the terminal value of the process at τ are given.",

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year = "2018",

doi = "10.1080/15326349.2018.1513335",

language = "English",

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T1 - A factorization of a Lévy process over a phase-type horizon

AU - Asmussen, Søren

AU - Ivanovs, Jevgenijs

PY - 2018

Y1 - 2018

N2 - This note provides a factorization of a Lévy pocess over a phase-type horizon τ given the phase at the supremum, thereby extending the Wiener–Hopf factorization for τ exponential. One of the factors is defined using time reversal of the phase process. It is shown that there are a variety of time-reversed representations, all yielding the same factor. Consequences of this are discussed and examples provided. Additionally, some explicit formulas for the joint law of the supremum and the terminal value of the process at τ are given.

AB - This note provides a factorization of a Lévy pocess over a phase-type horizon τ given the phase at the supremum, thereby extending the Wiener–Hopf factorization for τ exponential. One of the factors is defined using time reversal of the phase process. It is shown that there are a variety of time-reversed representations, all yielding the same factor. Consequences of this are discussed and examples provided. Additionally, some explicit formulas for the joint law of the supremum and the terminal value of the process at τ are given.

KW - phase-type distribution

KW - splitting

KW - time reversal

KW - Wiener–Hopf factorization

KW - WIENER-HOPF FACTORIZATION

KW - LAW

KW - MARKOV-ADDITIVE PROCESSES

KW - 1ST PASSAGE

KW - Wiener-Hopf factorization

KW - POSITIVE JUMPS

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DO - 10.1080/15326349.2018.1513335

M3 - Journal article

AN - SCOPUS:85059576138

SN - 1532-6349

VL - 34

SP - 397

EP - 408

JO - Stochastic Models

JF - Stochastic Models

IS - 4

ER -

A factorization of a Lévy process over a phase-type horizon

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Keywords

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