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

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  • Romain Biard

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    (LM-Besançon - Laboratoire de Mathématiques - CNRS : UMR6623 - Université de Franche-Comté)

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    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.

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    File URL: http://hal.archives-ouvertes.fr/docs/00/96/74/76/PDF/Biard2010.pdf
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    Bibliographic Info

    Paper provided by HAL in its series Post-Print with number hal-00538571.

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    Date of creation: 2013
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    Publication status: Published, Bulletin Français d'Actuariat, 2013, 13, 26, pp. 79-92
    Handle: RePEc:hal:journl:hal-00538571

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00538571
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    Web page: http://hal.archives-ouvertes.fr/

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

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    1. Stéphane Loisel, 2005. "Differentiation of some functionals of risk processes," Post-Print hal-00157739, HAL.
    2. 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.
    3. Cai, Jun & Li, Haijun, 2005. "Multivariate risk model of phase type," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 137-152, April.
    4. 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.
    5. 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.
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