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

Mathieu Bargès 1, 2 Stéphane Loisel 1 Xavier Venel 1, 3, 4
3 C&O - Equipe combinatoire et optimisation
UPMC - Université Pierre et Marie Curie - Paris 6, CNRS - Centre National de la Recherche Scientifique : FRE3232
Abstract : 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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Scandinavian Actuarial Journal, Taylor & Francis (Routledge), 2011, pp.xxx-xxx
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Mathieu Bargès, Stéphane Loisel, Xavier Venel. On finite-time ruin probabilities with reinsurance cycles influenced by large claims. Scandinavian Actuarial Journal, Taylor & Francis (Routledge), 2011, pp.xxx-xxx. 〈hal-00430178v2〉

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