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Stable Allocations of Risk

  • Peter Csoka


    (Department Economics, Universiteit of Maastricht)

  • P. Jean-Jacques Herings,


    (Department of Economics, Universiteit Maastricht,)

  • Laszlo A. Koczy


    (Department of Economics, Universiteit Maastricht,)

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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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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  1. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
  2. Péter Csóka & Jean-Jacques Herings & László Kóczy, 2006. "Coherent Measures of Risk from a General Equilibrium Perspective," IEHAS Discussion Papers 0611, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences, revised 30 Aug 2006.
  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. 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.
  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. 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).
  7. 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.
  8. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295,, revised May 2002.
  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. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
  11. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
  12. 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.
  13. Tijs, S.H. & Parthasarathy, T. & Potters, J.A.M. & Rajendra Prasad, V., 1984. "Permutation games : Another class of totally balanced games," Other publications TiSEM a7edfa18-6224-4be3-b677-5, Tilburg University, School of Economics and Management.
  14. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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