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On finite-time ruin probabilities with reinsurance cycles influenced by large claims

  • Mathieu Bargès


    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1, Ecole d'Actuariat - Universite Laval (Quebec))

  • Stéphane Loisel


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

  • Xavier Venel

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1, C&O - Equipe combinatoire et optimisation - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS, IMJ - Institut de Mathématiques de Jussieu - UPMC - Université Pierre et Marie Curie - Paris 6 - UP7 - Université Paris Diderot - Paris 7 - CNRS)

Market cycles play a great role in reinsurance. Cycle transitions are not independent from the claim arrival process : a large claim or a high number of claims may accelerate cycle transitions. To take this into account, a semi-Markovian risk model is proposed and analyzed. A refined Erlangization method is developed to compute the finite-time ruin probability of a reinsurance company. As this model needs the claim amounts to be Phase-type distributed, we explain how to fit mixtures of Erlang distributions to long-tailed distributions. Numerical applications and comparisons to results obtained from simulation methods are given. The impact of dependency between claim amounts and phase changes is studied.

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Paper provided by HAL in its series Post-Print with number hal-00430178.

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Date of creation: 2011
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Publication status: Published in Scandinavian Actuarial Journal, Taylor & Francis (Routledge), 2011,
Handle: RePEc:hal:journl:hal-00430178
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  1. De Vylder, F. Etienne & Goovaerts, Marc J., 1999. "Explicit finite-time and infinite-time ruin probabilities in the continuous case," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 155-172, May.
  2. Didier Rullière & Stéphane Loisel, 2004. "Another look at the Picard-Lefèvre formula for finite-time ruin probabilities," Post-Print hal-00379412, HAL.
  3. Stéphane Loisel & Claude Lefèvre, 2009. "Finite-Time Ruin Probabilities for Discrete, Possibly Dependent, Claim Severities," Post-Print hal-00201377, HAL.
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