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

Mathieu Bargès (1, 2) , Stéphane Loisel (1) , Xavier Venel (1, 3)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 Ecole d'Actuariat
3 C&O - Equipe combinatoire et optimisation

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.

Domaines: Economies et finances; Probabilités [math.PR]

Mathieu Bargès, Stéphane Loisel, Xavier Venel. On finite-time ruin probabilities with reinsurance cycles influenced by large claims. 2009. ⟨hal-00430178v1⟩