Coherent measures of risk from a general equilibrium perspective q Pe ´ter Cso ´ ka, P. Jean-Jacques Herings * ,1 , La ´szlo ´A ´ . Ko ´czy 2 Department of Economics, Universiteit Maastricht, P.O. Box 616, 6200 MD, Maastricht, The Netherlands Received 24 April 2006; accepted 24 October 2006 Available online 24 January 2007 Abstract Coherent measures of risk defined by the axioms of monotonicity, subadditivity, positive homo- geneity, and translation invariance are recent tools in risk management to assess the amount of risk agents are exposed to. If they also satisfy law invariance and comonotonic additivity, then we get a subclass of them: spectral measures of risk. Expected shortfall is a well-known spectral measure of risk. We investigate the above mentioned six axioms using tools from general equilibrium (GE) theory. Coherent and spectral measures of risk are compared to the natural measure of risk derived from an exchange economy model, which we call the GE measure of risk. We prove that GE measures of risk are coherent measures of risk. We also show that spectral measures of risk are GE measures of risk only under stringent conditions, since spectral measures of risk do not take the regulated entity’s relation to the market portfolio into account. To give more insights, we characterize the set of GE measures of risk via the pricing kernel property. Ó 2007 Elsevier B.V. All rights reserved. 0378-4266/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2006.10.026 q We are grateful to two anonymous referees and conference and seminar participants in Maastricht, Amsterdam, Budapest and Lisbon for helpful comments. * Corresponding author. Tel.: +31 43 388 3824; fax: +31 43 388 4878. E-mail addresses: P.Csoka@algec.unimaas.nl (P. Cso ´ ka), P.Herings@algec.unimaas.nl (P.J.-J. Herings), L.Koczy@algec.unimaas.nl (L.A ´ . Ko ´ czy). 1 The author would like to thank the Netherlands Organisation for Scientific Research (NWO) for financial support. 2 The author would like to thank funding by the Netherlands Organisation for Scientific Research (NWO) and by the European Union under the Marie Curie Intra-European Fellowship MEIF-CT-2004-011537. Journal of Banking & Finance 31 (2007) 2517–2534 www.elsevier.com/locate/jbf