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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

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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    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. 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.
    3. 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.

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    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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