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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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File URL: http://hdl.handle.net/10.1007/s00199-013-0753-3
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Article provided by Springer & Society for the Advancement of Economic Theory (SAET) 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. Nielsen, Lars Tyge, 1997. "Monotone Risk Aversion," CEPR Discussion Papers 1651, C.E.P.R. Discussion Papers.
  2. Robert J. Aumann & Roberto Serrano, 2007. "An economic index of riskiness," Working Papers 2007-08, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  3. James Cox & Vjollca Sadiraj & Bodo Vogt & Utteeyo Dasgupta, 2013. "Is there a plausible theory for decision under risk? A dual calibration critique," Economic Theory, Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 305-333, October.
  4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  5. repec:hal:journl:halshs-00211906 is not listed on IDEAS
  6. Chateauneuf, A. & Cohen, M. & Meilijson, I., 1997. "More Pessimism than Greediness: A Characterization of Monotone Risk Aversion in the Rank-Dependant Expected Utility Model," Papiers d'Economie Mathématique et Applications 97.53, Université Panthéon-Sorbonne (Paris 1).
  7. 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.
  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. Jon Eguia, 2013. "On the spatial representation of preference profiles," Economic Theory, Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 103-128, January.
  10. Yi-Chun Chen & Xiao Luo, 2012. "An indistinguishability result on rationalizability under general preferences," Economic Theory, Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 1-12, September.
  11. 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.
  12. 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.
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