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On Aumann and Serrano’s economic index of risk

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  • Minqiang Li

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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

Suggested Citation

  • 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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    References listed on IDEAS

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    1. Lars Nielsen, 2005. "Monotone risk aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 203-215.
    2. 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.
    3. Lars Nielsen, 2005. "Monotone risk aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 203-215.
    4. 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.
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    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. 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), pages 649-667.
    8. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
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    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. Jon Eguia, 2013. "On the spatial representation of preference profiles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 103-128.
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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), pages 309-331.

    More about this item

    Keywords

    Risk index; Attractiveness index; Duality; Additive gambles; Multiplicative gambles; C00; D80; D81;

    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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