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Explicit ruin formulas for models with dependence among risks


Author Info

  • Albrecher, Hansjörg
  • Constantinescu, Corina
  • Loisel, Stephane


We show that a simple mixing idea allows one to establish a number of explicit formulas for ruin probabilities and related quantities in collective risk models with dependence among claim sizes and among claim inter-occurrence times. Examples include compound Poisson risk models with completely monotone marginal claim size distributions that are dependent according to Archimedean survival copulas as well as renewal risk models with dependent inter-occurrence times.

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Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 48 (2011)
Issue (Month): 2 (March)
Pages: 265-270

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Handle: RePEc:eee:insuma:v:48:y:2011:i:2:p:265-270

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Keywords: Ruin probability Frailty models Mixing Archimedean copulas Completely monotone distributions;

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References listed on IDEAS
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  1. Alink, Stan & Lowe, Matthias & V. Wuthrich, Mario, 2004. "Diversification of aggregate dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 77-95, August.
  2. Ramsay, Colin M., 2003. "A solution to the ruin problem for Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 109-116, August.
  3. Albrecher, Hansjörg & Kortschak, Dominik, 2009. "On ruin probability and aggregate claim representations for Pareto claim size distributions," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 362-373, December.
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Cited by:
  1. 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.
  2. Landriault, David & Lemieux, Christiane & Willmot, Gordon E., 2012. "An adaptive premium policy with a Bayesian motivation in the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 370-378.
  3. repec:hal:wpaper:hal-00870224 is not listed on IDEAS
  4. Christophe Dutang & Claude Lefèvre & Stéphane Loisel, 2013. "On an asymptotic rule A+B/u for ultimate ruin probabilities under dependence by mixing," Post-Print hal-00746251, HAL.
  5. 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.
  6. Loisel, Stéphane & Trufin, Julien, 2014. "Properties of a risk measure derived from the expected area in red," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 191-199.
  7. Marri, Fouad & Furman, Edward, 2012. "Pricing compound Poisson processes with the Farlie–Gumbel–Morgenstern dependence structure," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 151-157.
  8. Stéphane Loisel & Julien Trufin, 2014. "Properties of a risk measure derived from the expected area in red," Post-Print hal-00870224, HAL.
  9. Peggy Cénac & Stéphane Loisel & Véronique Maume-Deschamps & Clémentine Prieur, 2013. "Risk indicators with several lines of business: comparison, asymptotic behavior and applications to optimal reserve allocation," Working Papers hal-00816894, HAL.
  10. repec:hal:wpaper:hal-00746251 is not listed on IDEAS
  11. Manel Kacem & Stéphane Loisel & Véronique Maume-Deschamps, 2012. "Some mixing properties of conditionally independent processes," Working Papers hal-00670649, HAL.


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