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Gerber-Shiu Metrics for a Bivariate Perturbed Risk Process

Author

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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
    Eurandom, Eindhoven University of Technology, 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
    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
    Amsterdam Business School, Faculty of Economics and Business, University of Amsterdam, 1090 GE Amsterdam, The Netherlands)

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.

Suggested Citation

  • Onno Boxma & Fabian Hinze & Michel Mandjes, 2023. "Gerber-Shiu Metrics for a Bivariate Perturbed Risk Process," Risks, MDPI, vol. 12(1), pages 1-17, December.
    • Handle: RePEc:gam:jrisks:v:12:y:2023:i:1:p:5-:d:1308826
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    References listed on IDEAS

    as
    1. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    2. Shuanming Li & Yi Lu & Kristina P. Sendova, 2019. "The expected discounted penalty function: from infinite time to finite time," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(4), pages 336-354, April.
    3. Dufresne, Francois & Gerber, Hans U., 1991. "Risk theory for the compound Poisson process that is perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 51-59, March.
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