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Stable Allocations of Risk

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  • Peter Csoka

    ()
    (Department Economics, Universiteit of Maastricht)

  • P. Jean-Jacques Herings,

    ()
    (Department of Economics, Universiteit Maastricht,)

  • Laszlo A. Koczy

    ()
    (Department of Economics, Universiteit Maastricht,)

Abstract

Measuring risk can be axiomatized by the concept of coherent measures of risk. A risk environment specifies some individual portfolios' realization vectors and a coherent measure of risk. We consider sharing the risk of the aggregate portfolio by studying transferable utility cooperative games: risk allocation games. We show that the class of risk allocation games coincides with the class of totally balanced games. As a limit case the aggregate portfolio can have the same payoff in all states of nature. We prove that the class of risk allocation games with no aggregate uncertainty coincides with the class of exact games.

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Bibliographic Info

Paper provided by Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences in its series IEHAS Discussion Papers with number 0704.

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Length: 23 pages
Date of creation: Sep 2007
Date of revision:
Handle: RePEc:has:discpr:0704

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Keywords: Coherent Measures of Risk; Risk Allocation Games; Totally Balanced Games; Exact Games;

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References

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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. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
  3. Ehud Kalai & Eitan Zemel, 1980. "Generalized Network Problems Yielding Totally Balanced Games," Discussion Papers 425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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. Hans Reijnierse & Jean Derks, 1998. "Note On the core of a collection of coalitions," International Journal of Game Theory, Springer, vol. 27(3), pages 451-459.
  6. Péter Csóka & P. Jean-Jacques Herings & László Á. Kóczy, 2007. "Balancedness Conditions for Exact Games," Working Paper Series 0805, Óbuda University, Keleti Faculty of Business and Management, revised May 2008.
  7. Ehud Kalai & Eitan Zemel, 1980. "On Totally Balanced Games and Games of Flow," Discussion Papers 413, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Herings,P. Jean-Jacques & Predtetchinski,Arkadi, 2002. "A Necessary and Sufficient Condition for Non--emptiness of the Core of a Non--transferable Utility Game," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  9. 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.
  10. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
  11. Csoka, Peter & Herings, P. Jean-Jacques & Koczy, Laszlo A., 2007. "Coherent measures of risk from a general equilibrium perspective," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2517-2534, August.
  12. Legut, Jerzy, 1990. "On totally balanced games arising from cooperation in fair division," Games and Economic Behavior, Elsevier, vol. 2(1), pages 47-60, March.
  13. Tijs, S.H. & Parthasarathy, T. & Potters, J.A.M. & Rajendra Prasad, V., 1984. "Permutation games: Another class of totally balanced games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154278, Tilburg University.
  14. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
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Citations

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Cited by:
  1. 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.
  2. Csóka, Péter & Herings, P. Jean-Jacques & Kóczy, László Á., 2007. "Balancedness Conditions for Exact Games," Research Memorandum 039, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. 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.
  4. Lohmann, E. & Borm, P. & Herings, P.J.J., 2012. "Minimal exact balancedness," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 127-135.
  5. Peter Csoka & P. Jean-Jacques Herings, 2013. "Risk Allocation under Liquidity Constraints," IEHAS Discussion Papers 1331, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  6. Csóka Péter & Herings P. Jean-Jacques & Kóczy László Á. & Pintér Miklós, 2009. "Convex and Exact Games with Non-transferable Utility," Research Memorandum 031, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  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.

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