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Risk Measures and Efficient use of Capital

Artzner, Philippe ; Delbaen, Freddy ; Koch-Medina, Pablo

In: ASTIN Bulletin, 2009, vol. 39, no. 1, p. 101-116

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    Title
    • Risk Measures and Efficient use of Capital
    Author
    • Artzner, Philippe. Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS et Laboratoire de Recherches en Gestion, FR 67084 Strasbourg, France, E-mail: artzner@math.u-strasbg.fr
    • Delbaen, Freddy. Departement für Mathematik, Eidgenössische Technische Hochschule, ETH-Zentrum, CH 8092 Zürich, Schweiz, E-mail: delbaen@math.ethz.ch
    • Koch-Medina, Pablo. Swiss Reinsurance Company, Mythenquai 50/60, CH 8022 Zürich, Schweiz, E-mail: Pablo_KochMedina@swissre.com
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:289245
    Summary
    This paper is concerned with clarifying the link between risk measurement and capital efficiency. For this purpose we introduce risk measurement as the minimum cost of making a position acceptable by adding an optimal combination of multiple eligible assets. Under certain assumptions, it is shown that these risk measures have properties similar to those of coherent risk measures. The motivation for this paper was the study of a multi-currency setting where it is natural to use simultaneously a domestic and a foreign asset as investment vehicles to inject the capital necessary to make an unacceptable position acceptable. We also study what happens when one changes the unit of account from domestic to foreign currency and are led to the notion of compatibility of risk measures. In addition, we aim to clarify terminology in the field