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Two parallel insurance lines with simultaneous arrivals and risks correlated with inter-arrival times

Author

Listed:
  • Badila, E.S.
  • Boxma, O.J.
  • Resing, J.A.C.

Abstract

We investigate an insurance risk model that consists of two reserves which receive income at fixed rates. Claims are being requested at random epochs from each reserve and the interclaim times are generally distributed. The two reserves are coupled in the sense that at a claim arrival epoch, claims are being requested from both reserves and the amounts requested are correlated. In addition, the claim amounts are correlated with the time elapsed since the previous claim arrival.

Suggested Citation

  • Badila, E.S. & Boxma, O.J. & Resing, J.A.C., 2015. "Two parallel insurance lines with simultaneous arrivals and risks correlated with inter-arrival times," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 48-61.
    • Handle: RePEc:eee:insuma:v:61:y:2015:i:c:p:48-61
    DOI: 10.1016/j.insmatheco.2014.12.003
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    References listed on IDEAS

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    1. Gong, Lan & Badescu, Andrei L. & Cheung, Eric C.K., 2012. "Recursive methods for a multi-dimensional risk process with common shocks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 109-120.
    2. Chan, Wai-Sum & Yang, Hailiang & Zhang, Lianzeng, 2003. "Some results on ruin probabilities in a two-dimensional risk model," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 345-358, July.
    3. Cai, Jun & Li, Haijun, 2005. "Multivariate risk model of phase type," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 137-152, April.
    4. Avram, Florin & Palmowski, Zbigniew & Pistorius, Martijn, 2008. "A two-dimensional ruin problem on the positive quadrant," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 227-234, February.
    5. V. G. Kulkarni, 1989. "A New Class of Multivariate Phase Type Distributions," Operations Research, INFORMS, vol. 37(1), pages 151-158, February.
    6. Sundt, Bjørn, 1999. "On Multivariate Panjer Recursions," ASTIN Bulletin, Cambridge University Press, vol. 29(1), pages 29-45, May.
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    Cited by:

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    5. Pablo Azcue & Nora Muler & Zbigniew Palmowski, 2016. "Optimal dividend payments for a two-dimensional insurance risk process," Papers 1603.07019, arXiv.org, revised Apr 2018.
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