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On Aumann and Serrano’s economic index of risk

  • Minqiang Li


We study the risk index of an additive gamble proposed in Aumann and Serrano (J Political Econ 116(5):810–836, 2008 ). We establish a generalized duality result for this index and use it to prove Yaari (J Econ Theory 1:315–329, 1969 ) alternative characterization of DARA utilities. A new characterization result for the risk index is obtained through essentially monotonic risk aversion utilities. We also extend the domain of gambles by introducing a price for gambles. We then develop a theory on the risk index for multiplicative gambles. Relative risk aversion functions for multiplicative gambles play the same role as absolute risk aversion functions for additive gambles. Copyright Springer-Verlag Berlin Heidelberg 2014

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Article provided by Springer in its journal Economic Theory.

Volume (Year): 55 (2014)
Issue (Month): 2 (February)
Pages: 415-437

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Handle: RePEc:spr:joecth:v:55:y:2014:i:2:p:415-437
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  1. James Cox & Vjollca Sadiraj & Bodo Vogt & Utteeyo Dasgupta, 2013. "Is there a plausible theory for decision under risk? A dual calibration critique," Economic Theory, Springer, vol. 54(2), pages 305-333, October.
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  3. Alain Chateauneuf & Michèle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the Rank-Dependent Expected Utility model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00211906, HAL.
  4. Nielsen, Lars Tyge, 1997. "Monotone Risk Aversion," CEPR Discussion Papers 1651, C.E.P.R. Discussion Papers.
  5. Robert J. Aumann & Roberto Serrano, 2007. "An Economic Index of Riskiness," Discussion Paper Series dp446, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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  8. Dybvig, Philip H & Lippman, Steven A, 1983. "An Alternative Characterization of Decreasing Absolute Risk Aversion," Econometrica, Econometric Society, vol. 51(1), pages 223-24, January.
  9. James C. Cox & Vjollca Sadiraj & Bodo Vogt & Utteeyo Dasgupta, 2007. "Is There A Plausible Theory for Risky Decisions?," Experimental Economics Center Working Paper Series 2007-05, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University, revised Apr 2008.
  10. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, 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.
  12. Yi-Chun Chen & Xiao Luo, 2012. "An indistinguishability result on rationalizability under general preferences," Economic Theory, Springer, vol. 51(1), pages 1-12, September.
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