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On an asymptotic rule A+B/u for ultimate ruin probabilities under dependence by mixing

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  • Dutang, C.
  • Lefèvre, C.
  • Loisel, S.

Abstract

The purpose of this paper is to point out that an asymptotic rule A+B/u for the ultimate ruin probability applies to a wide class of dependent risk processes, in continuous or discrete time. That dependence is incorporated through a mixing model in the individual claim amount distributions. Several special mixing distributions are examined in detail and some close-form formulas are derived. Claim tail distributions and the dependence structure are also investigated.

Suggested Citation

  • Dutang, C. & Lefèvre, C. & Loisel, S., 2013. "On an asymptotic rule A+B/u for ultimate ruin probabilities under dependence by mixing," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 774-785.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:774-785
    DOI: 10.1016/j.insmatheco.2013.09.020
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    Cited by:

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    2. Badía, F.G. & Sangüesa, C. & Cha, J.H., 2014. "Stochastic comparison of multivariate conditionally dependent mixtures," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 82-94.
    3. Buddana Amrutha & Kozubowski Tomasz J., 2014. "Discrete Pareto Distributions," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 143-156, December.
    4. Arendarczyk, Marek & Kozubowski, Tomasz. J. & Panorska, Anna K., 2018. "The joint distribution of the sum and maximum of dependent Pareto risks," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 136-156.
    5. Youri Raaijmakers & Hansjörg Albrecher & Onno Boxma, 2019. "The Single Server Queue with Mixing Dependencies," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1023-1044, December.

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