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Quantifizierung von Abhängigkeitsstrukturen zwischen Risiken in Versicherungsunternehmen

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Listed:
  • Nguyen, Tristan
  • Molinari, Robert Danilo

Abstract

Mit dem angedachten Solvabilitätssystem Solvency II werden Versicherer das erforderliche Solvenzkapital anhand ihrer tatsächlichen Risikosituation ermitteln müssen. Um diese zu bestimmen und zu quantifizieren, ist die Berücksichtigung der Abhängigkeiten zwischen den Risiken verschiedener Kategorien notwendig. Der vorliegende Beitrag beschreibt die Möglichkeiten, die hierfür zur Verfügung stehen. Neben der Erfassung von Abhängigkeiten zwischen Risiken durch den linearen Korrelationskoeffizienten nach Pearson ist auch deren Messung durch andere Kennzahlen, die demgegenüber gewisse Vorteile bieten, wie Spearman's Rangkorrelation oder Kendall's τ, denkbar. Einen völligen anderen Ansatz stellt das Konzept der Copulae bereit. Copulae ermöglichen eine vollständige Information über die Abhängigkeiten zwischen Risiken, indem durch ihre Anwendung die multivariate Verteilung der die Einzelrisiken beschreibenden Zufallsvariablen ermittelt werden kann. Dieses Konzept soll deshalb zunächst ausführlich erläutert werden, bevor auf seine mögliche Umsetzung in Versicherungsunternehmen eingegangen wird.

Suggested Citation

  • Nguyen, Tristan & Molinari, Robert Danilo, 2009. "Quantifizierung von Abhängigkeitsstrukturen zwischen Risiken in Versicherungsunternehmen," German Risk and Insurance Review (GRIR), University of Cologne, Department of Risk Management and Insurance, vol. 5(2), pages 28-52.
  • Handle: RePEc:zbw:grirej:68730
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    References listed on IDEAS

    as
    1. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    2. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    3. Thierry Ane & Cecile Kharoubi, 2003. "Dependence Structure and Risk Measure," The Journal of Business, University of Chicago Press, vol. 76(3), pages 411-438, July.
    4. Annalisa Di Clemente & Claudio Romano, 2004. "Measuring and Optimizing Portfolio Credit Risk: A Copula-based Approach," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 33(3), pages 325-357, November.
    5. Markus Junker & Angelika May, 2005. "Measurement of aggregate risk with copulas," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 428-454, December.
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