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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 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. Robert J. Aumann & Roberto Serrano, 2006. "An Economic Index of Riskiness," Working Papers 2006-20, Brown University, Department of Economics.
  2. 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.
  3. Yi-Chun Chen & Xiao Luo, 2012. "An indistinguishability result on rationalizability under general preferences," Economic Theory, Springer, vol. 51(1), pages 1-12, September.
  4. 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.
  5. Alain Chateauneuf & Michéle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model," Economic Theory, Springer, vol. 25(3), pages 649-667, 04.
  6. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  7. Lars Nielsen, 2005. "Monotone risk aversion," Economic Theory, Springer, vol. 25(1), pages 203-215, 01.
  8. repec:hal:journl:halshs-00211906 is not listed on IDEAS
  9. 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.
  10. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  11. Jon Eguia, 2013. "On the spatial representation of preference profiles," Economic Theory, Springer, vol. 52(1), pages 103-128, January.
  12. 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.
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