On finite-time ruin probabilities with reinsurance cycles influenced by large claims
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.
|Date of creation:||2011|
|Date of revision:|
|Publication status:||Published in Scandinavian Actuarial Journal, Taylor & Francis (Routledge), 2011, pp.xxx-xxx|
|Note:||View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00430178v2|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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- Didier Rullière & Stéphane Loisel, 2004.
"Another look at the Picard-Lefèvre formula for finite-time ruin probabilities,"
- Rulliere, Didier & Loisel, Stephane, 2004. "Another look at the Picard-Lefevre formula for finite-time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 187-203, October.
- Stéphane Loisel & Claude Lefèvre, 2009. "Finite-Time Ruin Probabilities for Discrete, Possibly Dependent, Claim Severities," Post-Print hal-00201377, HAL.
- 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.
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