Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-21T11:23:33.023Z Has data issue: false hasContentIssue false
  • English
  • Français

Risk Measures and Efficient use of Capital1

Published online by Cambridge University Press:  09 August 2013

Philippe Artzner ,
Freddy Delbaen  and
Pablo Koch-Medina
Philippe Artzner
Affiliation:
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
Freddy Delbaen
Affiliation:
Departement für Mathematik, Eidgenössische Technische Hochschule, ETH-Zentrum, CH 8092 Zürich, Schweiz, E-mail: delbaen@math.ethz.ch
Pablo Koch-Medina
Affiliation:
Swiss Reinsurance Company, Mythenquai 50/60, CH 8022 Zürich, Schweiz, E-mail: Pablo_KochMedina@swissre.com
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

Acceptance setaccountingcurrency compatibilityeligible assetno acceptability arbitragenon acceptability of leveragenumérairerisk-free investmentrisk measurementsupervision
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 1 , May 2009 , pp. 101 - 116
Copyright
Copyright © International Actuarial Association 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

2 Partial supports from AERF/CKER, The Actuarial Foundation and from the Isaac Newton Institute are gratefully acknowledged.
3 Partial support from Credit Suisse is gratefully acknowledged.
4 This author expresses his personal view in the paper.
1

This paper elaborates, with a major change, on presentations to the Isaac Newton Institute, DQF Program, February 2005, the Solvency II Tagung, University of Karlsruhe, April 2005, the ASTIN/AFIR Colloquium, Zürich, September 2005 and to the DGVFM Insurance Day, Cologne, April 2006. Thanks are due to referees for insisting on the need of comments related to the setting of the paper in the current literature, and to Jean-Marc Eber and Patrice Poncet for interesting discussions.

References

Artzner, Ph., Delbaen, F., Eber, J.-M. and Heath, D. (1997) Thinking coherently, Risk 10, 68–71.Google Scholar
Artzner, Ph., Delbaen, F., Eber, J.-M. and Heath, D. (1999) Coherent Risk Measures, Mathematical Finance 9, 203–228.CrossRefGoogle Scholar
Artzner, Ph., Delbaen, F., Eber, J.-M., Heath, D. and Ku, H. (2007) Coherent multiperiod risk-adjusted values and Bellman's principle, Annals of Operations Research 152, 5–22.CrossRefGoogle Scholar
Artzner, Ph., Delbaen, F., Koch-Medina, P. (2005) Risk Measures and Efficient Use of Capital, Proceedings 15th International AFIR Colloquium, Zürich, September 6-9.Google Scholar
Aumann, R. and Serrano, R. (2006) An Economic Index of Riskiness, Working paper, Department of Economics, Brown University.Google Scholar
Barrieu, P. and El Karoui, N. (2002) Optimal Risk Transfer, Working Paper, LSE and Ecole Polytechnique.Google Scholar
Barrieu, P. and El Karoui, N. (2005) Inf-convolution of risk measures and optimal risk transfer, Finance and Stochastics 9, 269–298.CrossRefGoogle Scholar
Committee of European Insurance and Occupational Pensions Supervisors (2007) Advice to the European Commission in the Framework of the Sovency II Project, March.Google Scholar
Delbaen, F. (2000) Coherent Risk Measures, Lectures Scuola Normale Superiore, Pisa.CrossRefGoogle Scholar
Dybvig, Ph. (1992) Hedging Nontraded Wealth: When is there Separation of Hedging and Investment?, Options: Recent Advances in Theory and Practice 2 (Hodges, S.D., ed.), Manchester University Press.Google Scholar
Filipovic, D. (2008) Optimal Numeraires for Risk Measures, Mathematical Finance 18, 333–336, earlier version December 2006.CrossRefGoogle Scholar
Föllmer, H. and Schied, A. (2004) Stochastic Finance, 2nd ed., de Gruyter, Berlin.CrossRefGoogle Scholar
Frittelli, M. and Scandolo, G. (2006) Risk measures and capital requirements for processes, Mathematical Finance 16, 589–612.CrossRefGoogle Scholar
Koch-Medina, P. (2006) Generalized coherent risk measures, Unpublished manuscript.Google Scholar
Rockafellar, T. (1970) Convex Analysis, Princeton University Press, Princeton, NJ.CrossRefGoogle Scholar
Stickney, C., Weil, R. and Davidson, S. (1991) Financial Accounting, 6th ed., Harcourt Brace Jovanovich, Orlando, FA.Google Scholar