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


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  • Christophe Dutang

    (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429, IRMA - Institut de Recherche Mathématique Avancée - CNRS : UMR7501 - Université de Strasbourg)

  • Claude Lefèvre

    (ULB - Département de Mathématique [Bruxelles] - Université Libre de Bruxelles)

  • Stéphane Loisel

    (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429)


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.

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Paper provided by HAL in its series Working Papers with number hal-00746251.

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Date of creation: 20 Jun 2013
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Handle: RePEc:hal:wpaper:hal-00746251

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  1. Stéphane Loisel & Claude Lefèvre, 2009. "Finite-Time Ruin Probabilities for Discrete, Possibly Dependent, Claim Severities," Post-Print hal-00201377, HAL.
  2. Hansjoerg Albrecher & Corina Constantinescu & Stéphane Loisel, 2011. "Explicit ruin formulas for models with dependence among risks," Post-Print hal-00540621, HAL.
  3. Julien Trufin & Stéphane Loisel, 2013. "Ultimate ruin probability in discrete time with Bühlmann credibility premium adjustments," Post-Print hal-00426790, HAL.
  4. Embrechts, P. & Veraverbeke, N., 1982. "Estimates for the probability of ruin with special emphasis on the possibility of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 55-72, January.
  5. Cai, Jun & Li, Haijun, 2005. "Multivariate risk model of phase type," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 137-152, April.
  6. Claude Lefèvre & Stéphane Loisel, 2008. "On Finite-Time Ruin Probabilities for Classical Risk Models," Post-Print hal-00168958, HAL.
  7. Albrecher, Hansjorg & Boxma, Onno J., 2004. "A ruin model with dependence between claim sizes and claim intervals," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 245-254, October.
  8. Centeno, Maria de Lourdes, 2002. "Measuring the effects of reinsurance by the adjustment coefficient in the Sparre Anderson model," Insurance: Mathematics and Economics, Elsevier, vol. 30(1), pages 37-49, February.
  9. Lefèvre, Claude & Picard, Philippe, 2011. "A new look at the homogeneous risk model," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 512-519.
  10. Dimitrova, Dimitrina S. & Kaishev, Vladimir K., 2010. "Optimal joint survival reinsurance: An efficient frontier approach," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 27-35, August.
  11. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
  12. Willmot, Gordon E., 1993. "Ruin probabilities in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 12(2), pages 133-142, April.
  13. Constantinescu, Corina & Hashorva, Enkelejd & Ji, Lanpeng, 2011. "Archimedean copulas in finite and infinite dimensions—with application to ruin problems," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 487-495.
  14. Centeno, Maria de Lourdes, 2002. "Excess of loss reinsurance and Gerber's inequality in the Sparre Anderson model," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 415-427, December.
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Cited by:
  1. Stéphane Loisel & Hans-U. Gerber, 2012. "Why ruin theory should be of interest for insurance practitioners and risk managers nowadays," Post-Print hal-00746231, HAL.


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