Coherent Measures of Risk from a General Equilibrium Perspective
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.
|Date of creation:||30 Aug 2006|
|Date of revision:||30 Aug 2006|
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Attila Ambrus & Rossella Argenziano, 2004.
"Network Markets and Consumer Coordination,"
CESifo Working Paper Series
1317, CESifo Group Munich.
- 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.
- Attila Ambrus & Rossella Argenziano, 2004. "Network Markets and Consumers Coordination," Cowles Foundation Discussion Papers 1481, Cowles Foundation for Research in Economics, Yale University.
- Dirk Tasche, 2002. "Expected Shortfall and Beyond," Papers cond-mat/0203558, arXiv.org, revised Oct 2002.
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
- 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.
- Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
- 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;International Association for the Study of Insurance Economics (The Geneva Association), vol. 15(1), pages 55-71, March.
- 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.
- 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.
- Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
- Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
- 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.
- 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.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Viktória Kocsis, 2005. "Network Asymmetries and Access Pricing in Cellular Telecommunications," Tinbergen Institute Discussion Papers 05-085/1, Tinbergen Institute.
- Stefan Jaschke & Uwe Küchler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, vol. 5(2), pages 181-200.
- LeRoy,Stephen F. & Werner,Jan, 2001. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9780521586054, October. Full references (including those not matched with items on IDEAS)