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Explicit ruin formulas for models with dependence among risks

Author

Listed:
  • Hansjoerg Albrecher

    (UNIL - Université de Lausanne)

  • Corina Constantinescu

    (UNIL - Université de Lausanne, SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Stéphane Loisel

    () (UNIL - Université de Lausanne, SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

We show that a simple mixing idea allows 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.

Suggested Citation

  • Hansjoerg Albrecher & Corina Constantinescu & Stéphane Loisel, 2011. "Explicit ruin formulas for models with dependence among risks," Post-Print hal-00540621, HAL.
  • Handle: RePEc:hal:journl:hal-00540621
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00540621
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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