Zusammenfassung
Der Begriff der stochastischen Dominanz erster, zweiter und dritter Ordnung spielt in der Nutzen-, Risiko- und Entscheidungstheorie eine wichtige Rolle. Er findet sich deshalb in Bereichen wieder, in denen diese Theorien Anwendung finden, so auch im finanzwirtschaftlichen Bereich. Auch im Zusammenhang mit der Performance-Messung risikobehafteter Anlagen spielt die stochastische Dominanz eine Rolle. Wir führen nachfolgend die Begriffe der stochastischen Dominanz erster, zweiter und dritter Ordnung ein und zeigen anschließend, wie man Dominanzbeziehungen empirischer Verteilungen untersucht.
Wir verwenden die folgende Notation. Seien X und Y zwei Zufallsvariablen mit zugehörigen Verteilungsfunktionen F und G. Inhaltlich stellen X und Y die Renditen (oder Überschussrenditen) zweier verschiedener, risikobehafteter Anlagen (einzelner Aktien oder Portfolios) dar, die miteinander verglichen werden sollen. Die Verteilungsfunktionen F(x) und G(y) beschreiben die Renditeverteilungen der beiden risikobehafteten Anlagen.
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(2006). Stochastische Dominanz. In: Finanzmarktstatistik. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29795-2_8
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