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

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  • 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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    Citations

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    Cited by:

    1. Boxma, Onno & Frostig, Esther & Perry, David & Yosef, Rami, 2017. "A state dependent reinsurance model," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 170-181.
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    3. Ivanovs, Jevgenijs & Boxma, Onno, 2015. "A bivariate risk model with mutual deficit coverage," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 126-134.
    4. 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.
    5. Gordienko, E. & Vázquez-Ortega, P., 2018. "Continuity inequalities for multidimensional renewal risk models," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 48-54.
    6. Zbigniew Palmowski, 2022. "First exit time for a discrete-time parallel queue," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 329-331, April.
    7. Albrecher, Hansjörg & Cheung, Eric C.K. & Liu, Haibo & Woo, Jae-Kyung, 2022. "A bivariate Laguerre expansions approach for joint ruin probabilities in a two-dimensional insurance risk process," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 96-118.
    8. Patch, Brendan & Nazarathy, Yoni & Taimre, Thomas, 2015. "A correction term for the covariance of renewal-reward processes with multivariate rewards," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 1-7.
    9. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2015. "Optimal Dividend Strategies for Two Collaborating Insurance Companies," Papers 1505.03980, arXiv.org.

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