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Asymptotic multivariate finite-time ruin probabilities with heavy-tailed claim amounts: Impact of dependence and optimal reserve allocation

Author

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  • Romain Biard

    () (LMB - Laboratoire de Mathématiques de Besançon - CNRS - Centre National de la Recherche Scientifique - UFC - Université de Franche-Comté)

Abstract

In ruin theory, the univariate model may be found too restrictive to describe accurately the complex evolution of the reserves of an insurance company. In the case where the company is composed of multiple lines of business, we compute asymptotics of finite-time ruin probabilities. Capital transfers between lines are partially allowed. When claim amounts are regularly varying distributed, several forms of dependence between the lines are considered. We also study the optimal allocation of a large global initial reserve in order to minimize the asymptotic ruin probability.

Suggested Citation

  • Romain Biard, 2013. "Asymptotic multivariate finite-time ruin probabilities with heavy-tailed claim amounts: Impact of dependence and optimal reserve allocation," Post-Print hal-00538571, HAL.
  • Handle: RePEc:hal:journl:hal-00538571
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00538571v2
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    File URL: https://hal.archives-ouvertes.fr/hal-00538571v2/document
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    References listed on IDEAS

    as
    1. Cai, Jun & Li, Haijun, 2007. "Dependence properties and bounds for ruin probabilities in multivariate compound risk models," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 757-773, April.
    2. Stéphane Loisel, 2005. "Differentiation of some functionals of risk processes," Post-Print hal-00157739, HAL.
    3. Biard, Romain & Lefèvre, Claude & Loisel, Stéphane, 2008. "Impact of correlation crises in risk theory: Asymptotics of finite-time ruin probabilities for heavy-tailed claim amounts when some independence and stationarity assumptions are relaxed," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 412-421, December.
    4. Cai, Jun & Li, Haijun, 2005. "Multivariate risk model of phase type," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 137-152, April.
    5. Romain Biard & Stéphane Loisel & Claudio Macci & Noel Veraverbeke, 2010. "Asymptotic behavior of the finite-time expected time-integrated negative part of some risk processes and optimal reserve allocation," Post-Print hal-00372525, HAL.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Multivariate finite-time ruin probabilities; Multivariate regular variation; Capital transfer; Optimal allocation;

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