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Stable allocations of risk

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Author Info
Csóka, Péter
Herings, P. Jean-Jacques
Kóczy, László Á.

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Abstract

The measurement and the allocation of risk are fundamental problems of portfolio management. Coherent measures of risk provide an axiomatic approach to the former problem. In an environment given by a coherent measure of risk and the various portfolios' realization vectors, risk allocation games aim at solving the second problem: How to distribute the diversification benefits of the various portfolios? Understanding these cooperative games helps us to find stable, efficient, and fair allocations of risk. We show that the class of risk allocation and totally balanced games coincide, hence a stable allocation of risk is always possible. When the aggregate portfolio is riskless, the class of risk allocation games coincides with the class of exact games. As in exact games any subcoalition may be subject to marginalization even in core allocations, our result further emphasizes the responsibility involved in allocating risk.

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File URL: http://www.sciencedirect.com/science/article/B6WFW-4V0MR4G-1/2/afb35495e15b20d615b087995899d874
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Publisher Info
Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 67 (2009)
Issue (Month): 1 (September)
Pages: 266-276
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Handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:266-276

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Web page: http://www.elsevier.com/locate/inca/622836

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Related research
Keywords: Coherent measures of risk Risk allocation games Totally balanced games Exact games;

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References listed on IDEAS
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.:
  1. Csóka, Péter & Herings, P. Jean-Jacques & Kóczy, László Á., 2007. "Balancedness Conditions for Exact Games," Research Memoranda 039, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
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  2. 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. [Downloadable!] (restricted)
  3. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
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  6. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
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  9. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July. [Downloadable!] (restricted)
  10. 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. [Downloadable!]
  11. 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. [Downloadable!]
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Cited by:
(explanations, 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.)

  1. Péter Csóka & P. Jean-Jacques Herings & László Á. Kóczy & Miklós Pintér, 2009. "Convex and Exact Games with Non-transferable Utility," Working Paper Series 0904, Budapest Tech, Keleti Faculty of Economics. [Downloadable!]
  2. Péter Csóka & P. Jean-Jacques Herings & László Á. Kóczy, 2007. "Balancedness Conditions for Exact Games," Working Paper Series 0805, Budapest Tech, Keleti Faculty of Economics, revised May 2008. [Downloadable!]
    Other versions:
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