Gerber-Shiu Metrics for a Bivariate Perturbed Risk Process

Onno Boxma, Fabian Hinze and Michel Mandjes ()
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Onno Boxma: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Fabian Hinze: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
Michel Mandjes: Eurandom, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands

Risks, 2023, vol. 12, issue 1, 1-17

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: Cramér–Lundberg model; Brownian perturbation; multivariate risk; ruin probability; Gerber–Shiu metrics (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
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