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The Foster-Hart measure of riskiness for general gambles

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  • Hellmann, Tobias

    ()
    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    ()
    (Center for Mathematical Economics, Bielefeld University)

Abstract

Foster and Hart propose a measure of riskiness for discrete random variables. 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. For many discrete gambles with a large number of values, the Foster--Hart riskiness is close to the maximal loss. We give a simple characterization of gambles whose riskiness is or is close to the maximal loss.

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Article provided by Econometric Society in its journal Theoretical Economics.

Volume (Year): (Forthcoming)
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Handle: RePEc:the:publsh:1499

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Keywords: Risk measures; operational; bankruptcy; continuous random variable;

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  1. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
  2. Robert J. Aumann & Roberto Serrano, 2006. "An Economic Index of Riskiness," Levine's Bibliography 321307000000000585, UCLA Department of Economics.
  3. Hart, Sergiu & Foster, Dean P., 2013. "A wealth-requirement axiomatization of riskiness," Theoretical Economics, Econometric Society, vol. 8(2), May.
  4. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617 - 638.
  5. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
  6. Dean P. Foster & Sergiu Hart, 2007. "An Operational Measure of Riskiness," Discussion Paper Series dp454, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  7. Turan G. Bali & Nusret Cakici & Fousseni Chabi-Yo, 2011. "A Generalized Measure of Riskiness," Management Science, INFORMS, vol. 57(8), pages 1406-1423, August.
  8. 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.
  9. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  10. 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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