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Closed-form and numerical computations of actuarial indicators in ruin theory and claim reserving

Author

Listed:
  • Alexandre Brouste

    (LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université)

  • Christophe Dutang

    (LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université)

Abstract

Insurance reserving is a key topic for both actuaries and academics. In the present paper, we present an efficient way to compute all the key indicators in a unified approach of the ruin theory and claim reserving methods. The proposed framework allows to derive closed-form formulas for both ruin theory and claim reserves indicators. A numerical illustration of these indicators is carried out on a real dataset from a private insurer. Résumé Le provisionnement en assurance non-vie est un sujet clé pour les actuaires et les académiques. Dans le présent article, nous présentons une méthode efficace pour calculer les indicateurs par une approche unifiée de la théorie de la ruine et du provisionnement non-vie. Le cadre proposé permet de déduire des formules fermées pour les indicateurs de provisionnement et de ruine. Une illustration de ces indicateurs est réalisée sur un jeu de données réellles. Mots-clés : théorie de la ruine, provisionnement non-vie, processus de Poisson, assurance non vie.

Suggested Citation

  • Alexandre Brouste & Christophe Dutang, 2016. "Closed-form and numerical computations of actuarial indicators in ruin theory and claim reserving," Post-Print hal-01616192, HAL.
    • Handle: RePEc:hal:journl:hal-01616192
    Note: View the original document on HAL open archive server: https://hal.science/hal-01616192v1
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    References listed on IDEAS

    as
    1. Larsen, Christian Roholte, 2007. "An Individual Claims Reserving Model," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 113-132, May.
    2. repec:cup:astinb:v:26:y:1996:i:02:p:139-164_00 is not listed on IDEAS
    3. Pigeon, Mathieu & Antonio, Katrien & Denuit, Michel, 2013. "Individual Loss Reserving With The Multivariate Skew Normal Framework," ASTIN Bulletin, Cambridge University Press, vol. 43(3), pages 399-428, September.
    4. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
    5. Norberg, Ragnar, 1999. "Prediction of Outstanding Liabilities II. Model Variations and Extensions," ASTIN Bulletin, Cambridge University Press, vol. 29(1), pages 5-25, May.
    6. repec:cup:astinb:v:19:y:1989:i:02:p:139-152_00 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

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