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Coherent Measures of Risk from a General Equilibrium Perspective

  • Péter Csóka

    ()

    (Department of Economics, Universiteit Maastricht)

  • Jean-Jacques Herings

    ()

    (Department of Economics, Universiteit Maastricht)

  • László Kóczy

    ()

    (Department of Economics, Universiteit Maastricht)

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 equi- librium (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 Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences in its series IEHAS Discussion Papers with number 0611.

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Date of creation: 30 Aug 2006
Date of revision: 30 Aug 2006
Handle: RePEc:has:discpr:0611
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  1. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
  2. Vikt�ria Kocsis, 2005. "Network Asymmetries and Access Pricing in Cellular Telecommunications," Tinbergen Institute Discussion Papers 05-085/1, Tinbergen Institute.
  3. John Geanakoplos & Martin Shubik, 1990. "The Capital Asset Pricing Model as a General Equilibrium With Incomplete Markets*," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 15(1), pages 55-71, March.
  4. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  5. Attila Ambrus & Rosella Argenziano, 2004. "Network Markets and Consumer Coordination," IEHAS Discussion Papers 0423, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  6. Stefan Jaschke & Uwe Küchler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, vol. 5(2), pages 181-200.
  7. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
  8. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, March.
  9. Kata Bognar & Lones Smith, 2004. "We Can't Argue Forever," IEHAS Discussion Papers 0415, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  10. 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.
  11. Vikt�ria Kocsis, 2005. "Network Asymmetries and Access Pricing in Cellular Telecommunications," Tinbergen Institute Discussion Papers 05-085/1, Tinbergen Institute.
  12. 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.
  13. John Geanakoplos & Martin Shubik, 1989. "The Capital Asset Pricing Model as a General Equilibrium with Incomplete Markets," Cowles Foundation Discussion Papers 913, Cowles Foundation for Research in Economics, Yale University.
  14. repec:cup:cbooks:9780521586054 is not listed on IDEAS
  15. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, 09.
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