On finite-time ruin probabilities with reinsurance cycles influenced by large claims
AbstractMarket 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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Bibliographic InfoPaper provided by HAL in its series Post-Print with number hal-00430178.
Date of creation: 2011
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Publication status: Published, Scandinavian Actuarial Journal, 2011, xxx-xxx
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-06-11 (All new papers)
- NEP-RMG-2011-06-11 (Risk Management)
- NEP-UPT-2011-06-11 (Utility Models & Prospect Theory)
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- 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.
- 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.
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