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The Foster-Hart Measure of Riskiness for General Gambles

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  • Frank Riedel

    (Bielefeld University)

  • Tobias Hellmann

    (Bielefeld University)

Abstract

Foster and Hart proposed an operational measure of riskiness for discrete random variables. We show that their defining equation has no solution for many common continuous distributions including many uniform distributions, e.g. We show how to extend consistently the definition of riskiness to continuous random variables. For many continuous random variables, the risk measure is equal to the worst case risk measure, i.e. the maximal possible loss incurred by that gamble. We also extend the Foster-Hart risk measure to dynamic environments for general distributions and probability spaces, and we show that the extended measure avoids bankruptcy in infinitely repeated gambles.

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File URL: http://www.imw.uni-bielefeld.de/n/upload/paper/74db120f0a8e5646ef5a30154e9f6deb.pdf
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 474.

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Length: 24 pages
Date of creation: Jan 2013
Date of revision:
Handle: RePEc:bie:wpaper:474

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  1. Homm, Ulrich & Pigorsch, Christian, 2012. "An operational interpretation and existence of the Aumann–Serrano index of riskiness," Economics Letters, Elsevier, vol. 114(3), pages 265-267.
  2. Dean P. Foster & Sergiu Hart, 2011. "A Wealth-Requirement Axiomatization of Riskiness," Discussion Paper Series dp577, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  3. Robert J. Aumann & Roberto Serrano, 2006. "An Economic Index of Riskiness," Levine's Bibliography 321307000000000585, UCLA Department of Economics.
  4. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
  5. Dean Foster & Sergiu Hart, 2007. "An Operational Measure of Riskiness," Levine's Bibliography 843644000000000095, UCLA Department of Economics.
  6. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617 - 638.
  7. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  9. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
  10. Turan G. Bali & Nusret Cakici & Fousseni Chabi-Yo, 2011. "A Generalized Measure of Riskiness," Management Science, INFORMS, vol. 57(8), pages 1406-1423, August.
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