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On Aumann and Serrano's Economic Index of Risk

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  • Li, Minqiang

Abstract

We study the risk index of an additive gamble proposed in Aumann and Serrano (2008).We establish a generalized duality result for this index and use it to prove Yaari's (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.

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File URL: http://mpra.ub.uni-muenchen.de/47466/1/MPRA_paper_47466.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 47466.

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Date of creation: 2013
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Handle: RePEc:pra:mprapa:47466
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Keywords: Risk index Attractiveness index Duality Additive gambles Multiplicative gambles;

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Find related papers by JEL classification:
  • C00 - Mathematical and Quantitative Methods - - General - - - General
  • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
  • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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  1. 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).
  2. Nielsen, Lars Tyge, 1997. "Monotone Risk Aversion," CEPR Discussion Papers 1651, C.E.P.R. Discussion Papers.
  3. 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.
  4. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  6. 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.
  7. Yi-Chun Chen & Xiao Luo, 2012. "An indistinguishability result on rationalizability under general preferences," Economic Theory, Springer, vol. 51(1), pages 1-12, September.
  8. repec:hal:journl:halshs-00211906 is not listed on IDEAS
  9. Jon Eguia, 2013. "On the spatial representation of preference profiles," Economic Theory, Springer, vol. 52(1), pages 103-128, January.
  10. 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.
  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. 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.
  13. 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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Cited by:

  1. Amnon Schreiber, 2014. "Economic indices of absolute and relative riskiness," Economic Theory, Springer, vol. 56(2), pages 309-331, June.
  2. Francis Mwesigye & Tomoya Matsumoto & Keijiro Otsuka, 2014. "Population Pressure, Rural-to-Rural Migration and Evolution of Land Tenure Institutions: The Case of Uganda," GRIPS Discussion Papers 14-09, National Graduate Institute for Policy Studies.

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