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The Foster-Hart Measure of Riskiness for General Gambles

  • Frank Riedel
  • Tobias Hellmann

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://arxiv.org/pdf/1301.1471
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Paper provided by arXiv.org in its series Papers with number 1301.1471.

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Date of creation: Jan 2013
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Handle: RePEc:arx:papers:1301.1471
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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. Tobias Hellmann & Frank Riedel, 2014. "A Dynamic Extension of the Foster-Hart Measure of Riskiness," Working Papers 528, Bielefeld University, Center for Mathematical Economics.
  3. Dean P. Foster & Sergiu Hart, 2011. "A Wealth-Requirement Axiomatization of Riskiness," Discussion Paper Series dp577, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  4. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
  5. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
  6. Sergiu Hart, 2010. "Comparing Risks by Acceptance and Rejection," Discussion Paper Series dp531, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  7. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785 - 814.
  8. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  9. Turan G. Bali & Nusret Cakici & Fousseni Chabi-Yo, 2011. "A Generalized Measure of Riskiness," Management Science, INFORMS, vol. 57(8), pages 1406-1423, August.
  10. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
  11. 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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