Matrix Mittag–Leffler distributions and modeling heavy-tailed risks

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Standard

Matrix Mittag–Leffler distributions and modeling heavy-tailed risks. / Albrecher, Hansjörg; Bladt, Martin; Bladt, Mogens.

I: Extremes, Bind 23, Nr. 3, 2020, s. 425-450.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Albrecher, H, Bladt, M & Bladt, M 2020, 'Matrix Mittag–Leffler distributions and modeling heavy-tailed risks', Extremes, bind 23, nr. 3, s. 425-450. https://doi.org/10.1007/s10687-020-00377-0

APA

Albrecher, H., Bladt, M., & Bladt, M. (2020). Matrix Mittag–Leffler distributions and modeling heavy-tailed risks. Extremes, 23(3), 425-450. https://doi.org/10.1007/s10687-020-00377-0

Vancouver

Albrecher H, Bladt M, Bladt M. Matrix Mittag–Leffler distributions and modeling heavy-tailed risks. Extremes. 2020;23(3):425-450. https://doi.org/10.1007/s10687-020-00377-0

Author

Albrecher, Hansjörg ; Bladt, Martin ; Bladt, Mogens. / Matrix Mittag–Leffler distributions and modeling heavy-tailed risks. I: Extremes. 2020 ; Bind 23, Nr. 3. s. 425-450.

Bibtex

@article{6fd47ef0c8874462aca54c4c66ad7a30,
title = "Matrix Mittag–Leffler distributions and modeling heavy-tailed risks",
abstract = "In this paper we define the class of matrix Mittag-Leffler distributions and study some of its properties. We show that it can be interpreted as a particular case of an inhomogeneous phase-type distribution with random scaling factor, and alternatively also as the absorption time of a semi-Markov process with Mittag-Leffler distributed interarrival times. We then identify this class and its power transforms as a remarkably parsimonious and versatile family for the modeling of heavy-tailed risks, which overcomes some disadvantages of other approaches like the problem of threshold selection in extreme value theory. We illustrate this point both on simulated data as well as on a set of real-life MTPL insurance data that were modeled differently in the past.",
keywords = "62E10, 62F10), 62P05 (33E12, 91G05, Heavy tails, Matrix distributions, Mittag-Leffler functions, Phase-type distributions, Random scaling, Risk modeling",
author = "Hansj{\"o}rg Albrecher and Martin Bladt and Mogens Bladt",
year = "2020",
doi = "10.1007/s10687-020-00377-0",
language = "English",
volume = "23",
pages = "425--450",
journal = "Extremes",
issn = "1386-1999",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - Matrix Mittag–Leffler distributions and modeling heavy-tailed risks

AU - Albrecher, Hansjörg

AU - Bladt, Martin

AU - Bladt, Mogens

PY - 2020

Y1 - 2020

N2 - In this paper we define the class of matrix Mittag-Leffler distributions and study some of its properties. We show that it can be interpreted as a particular case of an inhomogeneous phase-type distribution with random scaling factor, and alternatively also as the absorption time of a semi-Markov process with Mittag-Leffler distributed interarrival times. We then identify this class and its power transforms as a remarkably parsimonious and versatile family for the modeling of heavy-tailed risks, which overcomes some disadvantages of other approaches like the problem of threshold selection in extreme value theory. We illustrate this point both on simulated data as well as on a set of real-life MTPL insurance data that were modeled differently in the past.

AB - In this paper we define the class of matrix Mittag-Leffler distributions and study some of its properties. We show that it can be interpreted as a particular case of an inhomogeneous phase-type distribution with random scaling factor, and alternatively also as the absorption time of a semi-Markov process with Mittag-Leffler distributed interarrival times. We then identify this class and its power transforms as a remarkably parsimonious and versatile family for the modeling of heavy-tailed risks, which overcomes some disadvantages of other approaches like the problem of threshold selection in extreme value theory. We illustrate this point both on simulated data as well as on a set of real-life MTPL insurance data that were modeled differently in the past.

KW - 62E10

KW - 62F10)

KW - 62P05 (33E12

KW - 91G05

KW - Heavy tails

KW - Matrix distributions

KW - Mittag-Leffler functions

KW - Phase-type distributions

KW - Random scaling

KW - Risk modeling

UR - http://www.scopus.com/inward/record.url?scp=85085937155&partnerID=8YFLogxK

U2 - 10.1007/s10687-020-00377-0

DO - 10.1007/s10687-020-00377-0

M3 - Journal article

AN - SCOPUS:85085937155

VL - 23

SP - 425

EP - 450

JO - Extremes

JF - Extremes

SN - 1386-1999

IS - 3

ER -

ID: 243064745