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Reinsurance, ruin and solvency issues: some pitfalls

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  • Arthur Charpentier

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris, CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

Abstract

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.

Suggested Citation

  • Arthur Charpentier, 2010. "Reinsurance, ruin and solvency issues: some pitfalls," Working Papers hal-00463381, HAL.
    • Handle: RePEc:hal:wpaper:hal-00463381
    Note: View the original document on HAL open archive server: https://hal.science/hal-00463381
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    References listed on IDEAS

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    1. Dickson, David C. M. & Waters, Howard R., 1996. "Reinsurance and ruin," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 61-80, December.
    2. 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.
    3. Centeno, Lourdes, 1986. "Measuring the effects of reinsurance by the adjustment coefficient," Insurance: Mathematics and Economics, Elsevier, vol. 5(2), pages 169-182, April.
    4. 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.
    5. 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.
    6. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
    Full references (including those not matched with items on IDEAS)

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