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 af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

6 Citationer (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.

Originalsprog	Engelsk
Tidsskrift	Stochastic Models
Vol/bind	34
Nummer	4
Sider (fra-til)	397-408
Antal sider	12
ISSN	1532-6349
DOI	https://doi.org/10.1080/15326349.2018.1513335
Status	Udgivet - 2018

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10.1080/15326349.2018.1513335

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

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Citationsformater

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

AU - Asmussen, Søren

AU - Ivanovs, Jevgenijs

PY - 2018

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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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