Parisian types of ruin probabilities for a class of dependent risk-reserve processes

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Standard

Parisian types of ruin probabilities for a class of dependent risk-reserve processes. / Bladt, Mogens; Nielsen, Bo Friis; Peralta, Oscar.

I: Scandinavian Actuarial Journal, Bind 2019, Nr. 1, 02.01.2019, s. 32-61.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

Harvard

Bladt, M, Nielsen, BF & Peralta, O 2019, 'Parisian types of ruin probabilities for a class of dependent risk-reserve processes' Scandinavian Actuarial Journal, bind 2019, nr. 1, s. 32-61. https://doi.org/10.1080/03461238.2018.1483420

APA

Bladt, M., Nielsen, B. F., & Peralta, O. (2019). Parisian types of ruin probabilities for a class of dependent risk-reserve processes. Scandinavian Actuarial Journal, 2019(1), 32-61. https://doi.org/10.1080/03461238.2018.1483420

Vancouver

Bladt M, Nielsen BF, Peralta O. Parisian types of ruin probabilities for a class of dependent risk-reserve processes. Scandinavian Actuarial Journal. 2019 jan 2;2019(1):32-61. https://doi.org/10.1080/03461238.2018.1483420

Author

Bladt, Mogens ; Nielsen, Bo Friis ; Peralta, Oscar. / Parisian types of ruin probabilities for a class of dependent risk-reserve processes. I: Scandinavian Actuarial Journal. 2019 ; Bind 2019, Nr. 1. s. 32-61.

Bibtex

@article{0b5fe8ab661d433c908970433f50ed89,
title = "Parisian types of ruin probabilities for a class of dependent risk-reserve processes",
abstract = "For a rather general class of risk-reserve processes, we provide an exact method for calculating different kinds of ruin probabilities, with particular emphasis on variations over Parisian type of ruin. The risk-reserve processes under consideration have, in general, dependent phase-type distributed claim sizes and inter-arrivals times, whereas the movement between claims can either be linear or follow a Brownian motion with linear drift. For such processes, we provide explicit formulae for classical, Parisian and cumulative Parisian types of ruin (for both finite and infinite time horizons) when the clocks are phase-type distributed. An erlangization scheme provides an efficient algorithmic methods for calculating the aforementioned ruin probabilities with deterministic clocks. Special attention is drawn to the construction of specific dependency structures, and we provide a number of numerical examples to study its effect on probabilities.",
keywords = "(cumulative) Parisian ruin, Baker copula, Brownian motion, dependency, erlangization, fluid flow, L{\'e}vy process, order statistics, phase-type distributions, ruin probability, Sparre-Andersen",
author = "Mogens Bladt and Nielsen, {Bo Friis} and Oscar Peralta",
year = "2019",
month = "1",
day = "2",
doi = "10.1080/03461238.2018.1483420",
language = "English",
volume = "2019",
pages = "32--61",
journal = "Scandinavian Actuarial Journal",
issn = "0346-1238",
publisher = "Taylor & Francis Scandinavia",
number = "1",

}

RIS

TY - JOUR

T1 - Parisian types of ruin probabilities for a class of dependent risk-reserve processes

AU - Bladt, Mogens

AU - Nielsen, Bo Friis

AU - Peralta, Oscar

PY - 2019/1/2

Y1 - 2019/1/2

N2 - For a rather general class of risk-reserve processes, we provide an exact method for calculating different kinds of ruin probabilities, with particular emphasis on variations over Parisian type of ruin. The risk-reserve processes under consideration have, in general, dependent phase-type distributed claim sizes and inter-arrivals times, whereas the movement between claims can either be linear or follow a Brownian motion with linear drift. For such processes, we provide explicit formulae for classical, Parisian and cumulative Parisian types of ruin (for both finite and infinite time horizons) when the clocks are phase-type distributed. An erlangization scheme provides an efficient algorithmic methods for calculating the aforementioned ruin probabilities with deterministic clocks. Special attention is drawn to the construction of specific dependency structures, and we provide a number of numerical examples to study its effect on probabilities.

AB - For a rather general class of risk-reserve processes, we provide an exact method for calculating different kinds of ruin probabilities, with particular emphasis on variations over Parisian type of ruin. The risk-reserve processes under consideration have, in general, dependent phase-type distributed claim sizes and inter-arrivals times, whereas the movement between claims can either be linear or follow a Brownian motion with linear drift. For such processes, we provide explicit formulae for classical, Parisian and cumulative Parisian types of ruin (for both finite and infinite time horizons) when the clocks are phase-type distributed. An erlangization scheme provides an efficient algorithmic methods for calculating the aforementioned ruin probabilities with deterministic clocks. Special attention is drawn to the construction of specific dependency structures, and we provide a number of numerical examples to study its effect on probabilities.

KW - (cumulative) Parisian ruin

KW - Baker copula

KW - Brownian motion

KW - dependency

KW - erlangization

KW - fluid flow

KW - Lévy process

KW - order statistics

KW - phase-type distributions

KW - ruin probability

KW - Sparre-Andersen

UR - http://www.scopus.com/inward/record.url?scp=85049193535&partnerID=8YFLogxK

U2 - 10.1080/03461238.2018.1483420

DO - 10.1080/03461238.2018.1483420

M3 - Journal article

VL - 2019

SP - 32

EP - 61

JO - Scandinavian Actuarial Journal

JF - Scandinavian Actuarial Journal

SN - 0346-1238

IS - 1

ER -

ID: 203596060