Gerber-Shiu Metrics for a Bivariate Perturbed Risk Process

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

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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.

Original languageEnglish
Article number5
Number of pages17
JournalRisks
Volume12
Issue number1
DOIs
Publication statusPublished - Jan 2024

Funding

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

FundersFunder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek024.002.003

    Keywords

    • Brownian perturbation
    • Cramér–Lundberg model
    • Gerber–Shiu metrics
    • multivariate risk
    • ruin probability

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