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The Foster-Hart Measure of Riskiness for General Gambles

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  • Hellmann, Tobias
  • Riedel, Frank

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. 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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Paper provided by Verein für Socialpolitik / German Economic Association in its series Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order with number 79752.

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Date of creation: 2013
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Handle: RePEc:zbw:vfsc13:79752

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Web page: http://www.socialpolitik.org/
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  1. Roberto Serrano & Robert J. Aumann, 2007. "An Economic Index Of Riskiness," Working Papers, CEMFI wp2007_0706, CEMFI.
  2. Turan G. Bali & Nusret Cakici & Fousseni Chabi-Yo, 2011. "A Generalized Measure of Riskiness," Management Science, INFORMS, INFORMS, vol. 57(8), pages 1406-1423, August.
  3. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 117(5), pages 785 - 814.
  4. Hart, Sergiu & Foster, Dean P., 2013. "A wealth-requirement axiomatization of riskiness," Theoretical Economics, Econometric Society, Econometric Society, vol. 8(2), May.
  5. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 119(4), pages 617 - 638.
  6. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  7. Homm, Ulrich & Pigorsch, Christian, 2012. "An operational interpretation and existence of the Aumann–Serrano index of riskiness," Economics Letters, Elsevier, Elsevier, vol. 114(3), pages 265-267.
  8. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
  9. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
  10. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
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