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

Author

Listed:
  • Christophe Dutang

  • C. Lefevre

    (Département de mathématiques Université Libre de Bruxelles - ULB - Université libre de Bruxelles = Free University of Brussels)

  • S. Loisel

    (LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

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 models, in discrete and continuous time. Dependence is incorporated through a mixing approach among claim amounts or claim inter-arrival times, leading to a systemic risk behavior. Ruin corresponds here either to classical ruin, or to stopping the activity after realizing that it is not pro table at all, when one has little possibility to increase premium income rate. Several special cases for which closed formulas are derived, are also investigated in some detail.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Christophe Dutang & C. Lefevre & S. Loisel, 2013. "On an asymptotic rule A+B/u for ultimate ruin probabilities under dependence by mixing," Post-Print hal-01616175, HAL.
    • Handle: RePEc:hal:journl:hal-01616175
    DOI: 10.1016/j.insmatheco.2013.09.020
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    Cited by:

    1. Constantinescu Corina D. & Kozubowski Tomasz J. & Qian Haoyu H., 2019. "Probability of ruin in discrete insurance risk model with dependent Pareto claims," Dependence Modeling, De Gruyter, vol. 7(1), pages 215-233, January.
    2. Buddana Amrutha & Kozubowski Tomasz J., 2014. "Discrete Pareto Distributions," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 143-156, December.
    3. 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.
    4. 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.
    5. 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.

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