IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/47466.html
   My bibliography  Save this paper

On Aumann and Serrano's Economic Index of Risk

Author

Listed:
  • 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.

Suggested Citation

  • Li, Minqiang, 2013. "On Aumann and Serrano's Economic Index of Risk," MPRA Paper 47466, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:47466
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/47466/1/MPRA_paper_47466.pdf
    File Function: original version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Lars Nielsen, 2005. "Monotone risk aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(1), pages 203-215, January.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    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. 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.
    5. 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.
    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. 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.
    8. 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.
    9. 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.
    10. 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 Jul 2010.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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.
    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.

    More about this item

    Keywords

    Risk index Attractiveness index Duality Additive gambles Multiplicative gambles;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:47466. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter) or (Rebekah McClure). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.