Gerber-Shiu Metrics for a Bivariate Perturbed Risk Process

Risks, vol. 12, pp. 5

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.

Authors 3

1. Onno Boxma

   Eindhoven University of Technology

   Affiliation as printed

   Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

   Eurandom, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands

2. Fabian Hinze

   University of Amsterdam

   Affiliation as printed

   Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands

3. Michel Mandjes corresponding Aachen Mathematical Institute

   Leiden University · University of Amsterdam · Eindhoven University of Technology

   Affiliation as printed

   Amsterdam Business School, Faculty of Economics and Business, University of Amsterdam, 1090 GE Amsterdam, The Netherlands

   Eurandom, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands

   Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands

   Mathematical Institute, P.O. Box 9512, 2300 RA Leiden, The Netherlands