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Relationships Between Archimedean Copulas and Morgenstern Utility Functions

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Copula Theory and Its Applications

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 198))

Abstract

The (additive) generator of an Archimedean copula is a strictly decreasing and convex function, while Morgenstern utility functions (applying to risk aversion decision makers) are nondecreasing and concave. In this presentation, relationships between generators and utility functions are established. For some well known Archimedean copula families, links between the generator and the corresponding utility function are demonstrated. Some new copula families are derived from classes of utility functions which appeared in the literature, and their properties are discussed. It is shown how dependence properties of an Archimedean copula translate into properties of the utility function from which they are constructed.

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Author information

Authors and Affiliations

  1. Cass Business School, City University London, London, UK

    Jaap Spreeuw

Authors
  1. Jaap Spreeuw
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Correspondence to Jaap Spreeuw .

Editor information

Editors and Affiliations

  1. , Faculty of Mathematics Informatics, University of Warsaw, ul. Banacha 2, Warszawa, 02097, Poland

    Piotr Jaworski

  2. , Department of Knowledge-Based, Johannes Kepler Universität, Altenberger Straße 69, Linz, 4040, Austria

    Fabrizio Durante

  3. Ladislaus von Bortkiewicz Chair of Stati, C.A.S.E. Centre for Applied Statistics a, Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

  4. , Mathematical Institute, Polish Academy of Sciences, ul. Chopina 12, Toruń, 87100, Poland

    Tomasz Rychlik

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Spreeuw, J. (2010). Relationships Between Archimedean Copulas and Morgenstern Utility Functions. In: Jaworski, P., Durante, F., Härdle, W., Rychlik, T. (eds) Copula Theory and Its Applications. Lecture Notes in Statistics(), vol 198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12465-5_17

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