Gerber-Shiu Metrics for a Bivariate Perturbed Risk Process

Onno Boxma; Fabian Hinze; Michel Mandjes

doi:10.3390/risks12010005

Gerber-Shiu Metrics for a Bivariate Perturbed Risk Process

Onno Boxma, Fabian Hinze, Michel Mandjes (Corresponding author)

Stochastic Operations Research

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

24 Downloads (Pure)

Samenvatting

We consider a two-dimensional risk model with simultaneous Poisson arrivals of claims. Each claim of the first input process is at least as large as the corresponding claim of the second input process. In addition, the two net cumulative claim processes share a common Brownian motion component. For this model we determine the Gerber–Shiu metrics, covering the probability of ruin of each of the two reserve processes before an exponentially distributed time along with the ruin times and the undershoots and overshoots at ruin.

Originele taal-2	Engels
Artikelnummer	5
Aantal pagina's	17
Tijdschrift	Risks
Volume	12
Nummer van het tijdschrift	1
DOI's	https://doi.org/10.3390/risks12010005
Status	Gepubliceerd - jan. 2024

Financiering

The research of Onno Boxma and Michel Mandjes has been funded by the NWO Gravitation project Networks, grant number 024.002.003.

Financiers	Financiernummer
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	024.002.003

Toegang tot document

10.3390/risks12010005

pdfDefinitieve gepubliceerde versie, 641 KBLicentie: CC BY

Andere bestanden en links

Link naar publicatie in Scopus

Citeer dit

@article{657465e18fb34d7fb261eac8ecf4dd55,

title = "Gerber-Shiu Metrics for a Bivariate Perturbed Risk Process",

abstract = "We consider a two-dimensional risk model with simultaneous Poisson arrivals of claims. Each claim of the first input process is at least as large as the corresponding claim of the second input process. In addition, the two net cumulative claim processes share a common Brownian motion component. For this model we determine the Gerber–Shiu metrics, covering the probability of ruin of each of the two reserve processes before an exponentially distributed time along with the ruin times and the undershoots and overshoots at ruin.",

keywords = "Brownian perturbation, Cram{\'e}r–Lundberg model, Gerber–Shiu metrics, multivariate risk, ruin probability",

author = "Onno Boxma and Fabian Hinze and Michel Mandjes",

year = "2024",

month = jan,

doi = "10.3390/risks12010005",

language = "English",

volume = "12",

journal = "Risks",

issn = "2227-9091",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "1",

}

TY - JOUR

T1 - Gerber-Shiu Metrics for a Bivariate Perturbed Risk Process

AU - Boxma, Onno

AU - Hinze, Fabian

AU - Mandjes, Michel

PY - 2024/1

Y1 - 2024/1

N2 - We consider a two-dimensional risk model with simultaneous Poisson arrivals of claims. Each claim of the first input process is at least as large as the corresponding claim of the second input process. In addition, the two net cumulative claim processes share a common Brownian motion component. For this model we determine the Gerber–Shiu metrics, covering the probability of ruin of each of the two reserve processes before an exponentially distributed time along with the ruin times and the undershoots and overshoots at ruin.

AB - We consider a two-dimensional risk model with simultaneous Poisson arrivals of claims. Each claim of the first input process is at least as large as the corresponding claim of the second input process. In addition, the two net cumulative claim processes share a common Brownian motion component. For this model we determine the Gerber–Shiu metrics, covering the probability of ruin of each of the two reserve processes before an exponentially distributed time along with the ruin times and the undershoots and overshoots at ruin.

KW - Brownian perturbation

KW - Cramér–Lundberg model

KW - Gerber–Shiu metrics

KW - multivariate risk

KW - ruin probability

UR - http://www.scopus.com/inward/record.url?scp=85183445386&partnerID=8YFLogxK

U2 - 10.3390/risks12010005

DO - 10.3390/risks12010005

M3 - Article

AN - SCOPUS:85183445386

SN - 2227-9091

VL - 12

JO - Risks

JF - Risks

IS - 1

M1 - 5

ER -

Gerber-Shiu Metrics for a Bivariate Perturbed Risk Process

Samenvatting

Financiering

Toegang tot document

Andere bestanden en links

Vingerafdruk

Citeer dit