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Coherent measures of risk from a general equilibrium perspective

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  • Csoka, Peter
  • Herings, P. Jean-Jacques
  • Koczy, Laszlo A.

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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Article provided by Elsevier in its journal Journal of Banking & Finance.

Volume (Year): 31 (2007)
Issue (Month): 8 (August)
Pages: 2517-2534

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Handle: RePEc:eee:jbfina:v:31:y:2007:i:8:p:2517-2534

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Cited by:
  1. Peter Csoka & Miklos Pinter, 2011. "On the Impossibility of Fair Risk Allocation," IEHAS Discussion Papers 1117, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  2. Csóka, Péter & Herings, P. Jean-Jacques & Kóczy, László Á,, 2007. "Stable Allocations of Risk," Research Memorandum 040, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. Shahid Ebrahim, M. & Hussain, Sikandar, 2010. "Financial development and asset valuation: The special case of real estate," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 150-162, January.
  4. Herings P.J.J. & Csóka P., 2013. "Risk allocation under liquidity constraints," Research Memorandum 057, Maastricht University, Graduate School of Business and Economics (GSBE).
  5. Kountzakis, C. & Polyrakis, I.A., 2013. "Coherent risk measures in general economic models and price bubbles," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 201-209.
  6. Nicos Scordis, 2011. "The Morality of Risk Modeling," Journal of Business Ethics, Springer, vol. 103(1), pages 7-16, April.
  7. Dora Balog, 2011. "Capital allocation in financial institutions: the Euler method," IEHAS Discussion Papers 1126, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  8. Csóka, Péter & Bátyi, Tamás László & Pintér, Miklós & Balog, Dóra, 2011. "Tőkeallokációs módszerek és tulajdonságaik a gyakorlatban
    [Methods of capital allocation and their characteristics in practice]
    ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 619-632.

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