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Reinsurance, ruin and solvency issues: some pitfalls

Listed author(s):
  • Arthur Charpentier

    (Department of Economics, Ecole Polytechnique - Polytechnique - X - CNRS - Centre National de la Recherche Scientifique, CREM - Centre de Recherche en Economie et Management - UNICAEN - Université Caen Normandie - UR1 - Université de Rennes 1 - CNRS - Centre National de la Recherche Scientifique)

In this paper, we consider optimal reinsurance from an insurer's point of view. Given a (low) ruin probability target, insurers want to find the optimal risk transfer mechanism, i.e. either a proportional or a nonproportional reinsurance treaty. Since it is usually admitted that reinsurance should lower ruin probabilities, it should be easy to derive an efficient Monte Carlo algorithm to link ruin probability and reinsurance parameter. Unfortunately, if it is possible for proportional reinsurance, this is no longer the case in nonproportional reinsurance. Some examples where reinsurance might increase ruin probabilities are given at the end, when claim arrival and claim size are not independent.

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Paper provided by HAL in its series Working Papers with number hal-00463381.

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Date of creation: 12 Mar 2010
Handle: RePEc:hal:wpaper:hal-00463381
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  1. Centeno, Lourdes, 1986. "Measuring the effects of reinsurance by the adjustment coefficient," Insurance: Mathematics and Economics, Elsevier, vol. 5(2), pages 169-182, April.
  2. Malinovskii, Vsevolod K., 1998. "Non-Poissonian claims' arrivals and calculation of the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 22(2), pages 123-138, June.
  3. Dickson, David C. M. & Waters, Howard R., 1996. "Reinsurance and ruin," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 61-80, December.
  4. Albrecher, Hansjorg & Boxma, Onno J., 2004. "A ruin model with dependence between claim sizes and claim intervals," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 245-254, October.
  5. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400, September.
  6. Gyllenberg, Mats & S. Silvestrov, Dmitrii, 2000. "Cramer-Lundberg approximation for nonlinearly perturbed risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 75-90, February.
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