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

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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Submitted on : Saturday, May 14, 2011 - 3:08:40 PM
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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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