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Aggregation in einem Risikoportfolio mit Abhängigkeitsstruktur

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  • Knobloch, Ralf

Abstract

Unternehmen sehen sich üblicherweise den unterschiedlichsten operativen und strategischen Risiken ausgesetzt. Daher ist das Risikoportfolio eines Unternehmens aus Sicht des betriebswirtschaftlichen Risikomanagement i.d.R. sehr inhomogen bezüglich der verwendeten Verteilungsmodelle. Neben der Bewertung der Einzelrisiken ist es die Aufgabe des quantitativen Risikomanagements, alle Einzelrisiken in einer Risikokennzahl (z.B. Value at Risk oder Expected Shortfall) zu aggregieren. Dazu werden Szenarien (mit einer Monte-Carlo-Simulation) simuliert, so dass die Verteilung des Gesamtrisikos mit Risikokennzahlen aggregiert und analysiert werden kann. Dabei muss zusätzlich die Abhängigkeitsstruktur der Einzelrisiken modelliert werden. Ein möglicher Ansatz zur Modellierung der Abhängigkeitsstruktur ist die Vorgabe einer Korrelationsmatrix. Der vorliegende Artikel beschäftigt anhand von Beispielen zum einen mit Konzepten und Methoden einer solchen Modellierung und zum anderen mit den Schwierigkeiten, die damit verbunden sind. Es zeigt sich, dass man bei der Wahl einer Korrelationsmatrix verschiedene Einschränkungen zu beachten hat. Ferner kann es zu einer vorgegebenen Korrelationsmatrix mehrere passende gemeinsame Verteilungen der Einzelrisken geben. Dies hat zur Folge, dass die Aggregation der Einzelrisiken in einer Risikokennzahl aus mathematischer Sicht nicht eindeutig ist.

Suggested Citation

  • Knobloch, Ralf, 2024. "Aggregation in einem Risikoportfolio mit Abhängigkeitsstruktur," Forschung am ivwKöln 2/2024, Technische Hochschule Köln – University of Applied Sciences, Institute for Insurance Studies.
    • Handle: RePEc:zbw:thkivw:284399
    DOI: 10.57684/COS-1234
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    References listed on IDEAS

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    1. Dhaene, Jan & Goovaerts, Marc J., 1996. "Dependency of Risks and Stop-Loss Order1," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 201-212, November.
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    More about this item

    Keywords

    Quantitatives Risikomanagement; Value at Risk; Korrelationsmatrix; Risikoaggregation; Fréchet-Hoeffding-Schranken; Quantitative Risk Management; Value at Risk; Correlation Matrix; Risk Aggregation; Fréchet-Hoeffding-Bounds;
    All these keywords.

    JEL classification:

    • G - Financial Economics
    • G2 - Financial Economics - - Financial Institutions and Services
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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