IDEAS home Printed from https://ideas.repec.org/p/has/discpr/0611.html
   My bibliography  Save this paper

Coherent Measures of Risk from a General Equilibrium Perspective

Author

Listed:
  • Péter Csóka

    (Department of Economics, Universiteit Maastricht)

  • Jean-Jacques Herings

    (Department of Economics, Universiteit Maastricht)

  • László Kóczy

    (Department of Economics, Universiteit Maastricht)

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 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.

Suggested Citation

  • Péter Csóka & Jean-Jacques Herings & László Kóczy, 2006. "Coherent Measures of Risk from a General Equilibrium Perspective," CERS-IE WORKING PAPERS 0611, Institute of Economics, Centre for Economic and Regional Studies, revised 30 Aug 2006.
    • Handle: RePEc:has:discpr:0611
    as

    Download full text from publisher

    File URL: http://econ.core.hu/doc/dp/dp/mtdp0611.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Koczy, Laszlo A. & Lauwers, Luc, 2007. "The minimal dominant set is a non-empty core-extension," Games and Economic Behavior, Elsevier, vol. 61(2), pages 277-298, November.
    2. Attila Ambrus & Rosella Argenziano, 2004. "Network Markets and Consumer Coordination," CERS-IE WORKING PAPERS 0423, Institute of Economics, Centre for Economic and Regional Studies.
    3. Anders Frederiksen & Elod Takats, 2004. "Optimal incentive mix of performance pay and efficiency wage," CERS-IE WORKING PAPERS 0418, Institute of Economics, Centre for Economic and Regional Studies.
    4. Dirk Tasche, 2002. "Expected Shortfall and Beyond," Papers cond-mat/0203558, arXiv.org, revised Oct 2002.
    5. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, Decembrie.
    6. Miklos Koren, 2004. "The law of two prices: trade costs and relative price variability," CERS-IE WORKING PAPERS 0422, Institute of Economics, Centre for Economic and Regional Studies.
    7. Koczy, Laszlo A., 2006. "The core can be accessed with a bounded number of blocks," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 56-64, December.
    8. Gabor Bekes & Balazs Murakozy, 2005. "Firm behaviour and public infrastructure - The Case of Hungary," CERS-IE WORKING PAPERS 0504, Institute of Economics, Centre for Economic and Regional Studies.
    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.
    10. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
    11. 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.
    12. Kata Bognar & Lones Smith, 2004. "We Can't Argue Forever," CERS-IE WORKING PAPERS 0415, Institute of Economics, Centre for Economic and Regional Studies.
    13. 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.
    14. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    15. 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.
    16. 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, September.
    17. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    18. Viktória Kocsis, 2005. "Network Asymmetries and Access Pricing in Cellular Telecommunications," Tinbergen Institute Discussion Papers 05-085/1, Tinbergen Institute.
    19. Peter Vida, 2005. "A Detail-free Mediator and the 3 Player Case," CERS-IE WORKING PAPERS 0511, Institute of Economics, Centre for Economic and Regional Studies.
    20. Julia Lendvai, 2004. "Inflation Inertia and Monetary Policy Shocks," CERS-IE WORKING PAPERS 0417, Institute of Economics, Centre for Economic and Regional Studies.
    21. Attila Ambrus & Rossella Argenziano, 2004. "Network Markets and Consumers Coordination," Cowles Foundation Discussion Papers 1481, Cowles Foundation for Research in Economics, Yale University.
    22. Stefan Jaschke & Uwe Küchler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, vol. 5(2), pages 181-200.
    23. LeRoy,Stephen F. & Werner,Jan, 2014. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9781107024120, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Csóka, Péter & Herings, P. Jean-Jacques, 2014. "Risk allocation under liquidity constraints," Journal of Banking & Finance, Elsevier, vol. 49(C), pages 1-9.
    2. Dávid Csercsik & László Á. Kóczy, 2017. "Efficiency and Stability in Electrical Power Transmission Networks: a Partition Function Form Approach," Networks and Spatial Economics, Springer, vol. 17(4), pages 1161-1184, December.
    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. Csóka, Péter & Herings, P. Jean-Jacques & Kóczy, László Á., 2009. "Stable allocations of risk," Games and Economic Behavior, Elsevier, vol. 67(1), pages 266-276, September.
    5. Zsolt Bihary & Péter Csóka & Dávid Zoltán Szabó, 2020. "Spectral risk measure of holding stocks in the long run," Annals of Operations Research, Springer, vol. 295(1), pages 75-89, December.
    6. 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.
    7. Péter Csóka & P. Herings & László Kóczy, 2011. "Balancedness conditions for exact games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(1), pages 41-52, August.
    8. Bernardi Mauro & Roy Cerqueti & Arsen Palestini, 2016. "Allocation of risk capital in a cost cooperative game induced by a modified Expected Shortfall," Papers 1608.02365, arXiv.org.
    9. Ormos Mihály & Timotity Dusán, 2017. "The Case of “Less is More”: Modelling Risk-Preference with Expected Downside Risk," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 17(2), pages 1-14, June.
    10. Csóka Péter & Pintér Miklós, 2016. "On the Impossibility of Fair Risk Allocation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(1), pages 143-158, January.
    11. Csóka, Péter & Bihary, Zsolt & Kondor, Gábor, 2018. "A részvénytartás spektrális kockázata hosszú távon [On the spectral measure of risk in holding stocks in the long run]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 687-700.
    12. Dóra Balog & Tamás László Bátyi & Péter Csóka & Miklós Pintér, 2014. "Properties of risk capital allocation methods: Core Compatibility, Equal Treatment Property and Strong Monotonicity," CERS-IE WORKING PAPERS 1417, Institute of Economics, Centre for Economic and Regional Studies.
    13. Dora Balog, 2011. "Capital allocation in financial institutions: the Euler method," CERS-IE WORKING PAPERS 1126, Institute of Economics, Centre for Economic and Regional Studies.
    14. Laszlo A. Koczy, 2019. "The risk-based core for cooperative games with uncertainty," CERS-IE WORKING PAPERS 1906, Institute of Economics, Centre for Economic and Regional Studies.
    15. Nicos Scordis, 2011. "The Morality of Risk Modeling," Journal of Business Ethics, Springer, vol. 103(1), pages 7-16, April.
    16. 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.
    17. Annette Hofmann & Nicos A. Scordis, 2018. "Challenges in Applying Risk Management Concepts in Practice: A Perspective," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 21(2), pages 309-333, September.
    18. Dóra Balog, 2010. "Risk based capital allocation," Proceedings of FIKUSZ '10, in: László Áron Kóczy (ed.),Proceedings of FIKUSZ 2010, pages 17-26, Óbuda University, Keleti Faculty of Business and Management.
    19. Balog, Dóra & Bátyi, Tamás László & Csóka, Péter & Pintér, Miklós, 2017. "Properties and comparison of risk capital allocation methods," European Journal of Operational Research, Elsevier, vol. 259(2), pages 614-625.
    20. Edina Berlinger & Kata Váradi, 2015. "Risk Appetite," Public Finance Quarterly, State Audit Office of Hungary, vol. 60(1), pages 49-62.
    21. Hevér, Judit, 2020. "A piaci likviditás és a szabályozás kapcsolatának vizsgálata általános egyensúlyelméleti modellkeretben [The effect of regulation on market liquidity: a general equilibrium approach]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 708-733.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gabor Virag, 2006. "Outside offers and bidding costs," CERS-IE WORKING PAPERS 0610, Institute of Economics, Centre for Economic and Regional Studies, revised 30 Aug 2006.
    2. Iván Major, 2006. "Why do (or do not) banks share customer information? A comparison of mature private credit markets and markets in transition," CERS-IE WORKING PAPERS 0603, Institute of Economics, Centre for Economic and Regional Studies, revised 24 Apr 2006.
    3. András Simonovits, 2006. "Social Security Reform in the US: Lessons from Hungary," CERS-IE WORKING PAPERS 0602, Institute of Economics, Centre for Economic and Regional Studies, revised 24 Apr 2006.
    4. Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Scholarly Articles 2624460, Harvard University Department of Economics.
    5. Wächter, Hans Peter & Mazzoni, Thomas, 2013. "Consistent modeling of risk averse behavior with spectral risk measures," European Journal of Operational Research, Elsevier, vol. 229(2), pages 487-495.
    6. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    7. Szego, Giorgio, 2005. "Measures of risk," European Journal of Operational Research, Elsevier, vol. 163(1), pages 5-19, May.
    8. Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2551-2569, August.
    9. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
    10. Chen, Zhiping & Wang, Yi, 2008. "Two-sided coherent risk measures and their application in realistic portfolio optimization," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2667-2673, December.
    11. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, Michael, 2006. "Master funds in portfolio analysis with general deviation measures," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 743-778, February.
    12. Dimitrios G. Konstantinides & Georgios C. Zachos, 2019. "Exhibiting Abnormal Returns Under a Risk Averse Strategy," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 551-566, June.
    13. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    14. Alexandre Kurth & Dirk Tasche, 2002. "Credit Risk Contributions to Value-at-Risk and Expected Shortfall," Papers cond-mat/0207750, arXiv.org, revised Nov 2002.
    15. Albrecht, Peter, 2003. "Risk measures," Papers 03-01, Sonderforschungsbreich 504.
    16. Dominique Guegan & Bertrand K Hassani, 2014. "Distortion Risk Measures or the Transformation of Unimodal Distributions into Multimodal Functions," Documents de travail du Centre d'Economie de la Sorbonne 14008, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    17. Weiwei Li & Dejian Tian, 2023. "Robust optimized certainty equivalents and quantiles for loss positions with distribution uncertainty," Papers 2304.04396, arXiv.org.
    18. Gordy, Michael B., 2003. "A risk-factor model foundation for ratings-based bank capital rules," Journal of Financial Intermediation, Elsevier, vol. 12(3), pages 199-232, July.
    19. Boonen, Tim J. & De Waegenaere, Anja & Norde, Henk, 2020. "A generalization of the Aumann–Shapley value for risk capital allocation problems," European Journal of Operational Research, Elsevier, vol. 282(1), pages 277-287.
    20. Joaquin, Domingo Castelo, 2009. "Value at risk: Is a theoretically consistent axiomatic formulation possible?," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(2), pages 725-729, May.

    More about this item

    Keywords

    Coherent Measures of Risk; General Equilibrium Theory; Exchange Economies; Asset Pricing;
    All these keywords.

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:has:discpr:0611. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Nora Horvath (email available below). General contact details of provider: https://edirc.repec.org/data/iehashu.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.