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On Aumann and Serrano’s economic index of risk

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  • Minqiang Li

Abstract

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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  • Minqiang Li, 2014. "On Aumann and Serrano’s economic index of risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 415-437, February.
    • Handle: RePEc:spr:joecth:v:55:y:2014:i:2:p:415-437
    DOI: 10.1007/s00199-013-0753-3
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    1. 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.
    2. 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;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 649-667, April.
    3. Lars Tyge Nielsen, 2006. "Monotone Risk Aversion," Studies in Economic Theory, in: Christian Schultz & Karl Vind (ed.), Institutions, Equilibria and Efficiency, chapter 17, pages 317-329, Springer.
    4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    5. Yi-Chun Chen & Xiao Luo, 2012. "An indistinguishability result on rationalizability under general preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 1-12, September.
    6. Dybvig, Philip H & Lippman, Steven A, 1983. "An Alternative Characterization of Decreasing Absolute Risk Aversion," Econometrica, Econometric Society, vol. 51(1), pages 223-224, January.
    7. 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 Jun 2012.
    8. 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.
    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;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 305-333, October.
    10. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    11. Jon Eguia, 2013. "On the spatial representation of preference profiles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 103-128, January.
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    Cited by:

    1. 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.
    2. Amnon Schreiber, 2014. "Economic indices of absolute and relative riskiness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 309-331, June.
    3. Minqiang Li, 2014. "Aumann and Serrano's economic index of risk for sums of gambles," Cogent Economics & Finance, Taylor & Francis Journals, vol. 2(1), pages 1-5, December.

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    More about this item

    Keywords

    Risk index; Attractiveness index; Duality; Additive gambles; Multiplicative gambles; C00; D80; D81;
    All these keywords.

    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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