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Coherent Measures of Risk from a General Equilibrium Perspective

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Author Info
Csóka, Péter
Herings, P. Jean-Jacques
Kóczy, László Á. (METEOR)

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Abstract

Coherent measures of risk defined by the axioms of monotonicity, subadditivity, positive homogeneity, 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 is. 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, that we call GE measure of risk. We prove that GE measures of risk are coherent measures of risk.We also show that spectral measures of risk can be represented by 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.

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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 016.

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Date of creation: 2006
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Handle: RePEc:dgr:umamet:2006016

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Keywords: microeconomics ;

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  2. Attila Ambrus & Rossella Argenziano, 2004. "Network Markets and Consumers Coordination," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
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  3. Kata Bognar & Lones Smith, 2004. "We Can't Argue Forever," IEHAS Discussion Papers 0415, Institute of Economics, Hungarian Academy of Sciences. [Downloadable!]
  4. John Geanakoplos & Martin Shubik, 1989. "The Capital Asset Pricing Model as a General Equilibrium with Incomplete Markets," Cowles Foundation Discussion Papers 913, Cowles Foundation, Yale University. [Downloadable!]
  5. Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, vol. 45(2), pages 427-38, March. [Downloadable!] (restricted)
  6. Rothkopf, Michael H. & Harstad, Ronald M., 1994. "On the role of discrete bid levels in oral auctions," European Journal of Operational Research, Elsevier, vol. 74(3), pages 572-581, May. [Downloadable!] (restricted)
  7. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July. [Downloadable!] (restricted)
  8. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July. [Downloadable!] (restricted)
  9. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier. [Downloadable!] (restricted)
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  1. Péter Csóka & P. Jean-Jacques Herings & László Á. Kóczy, 2007. "Stable Allocations of Risk," Working Paper Series 0802, Budapest Tech, Keleti Faculty of Economics, revised Apr 2008. [Downloadable!]
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