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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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Bibliographic Info

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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  1. Robert J. Aumann & Roberto Serrano, 2006. "An Economic Index of Riskiness," Working Papers, Brown University, Department of Economics 2006-20, Brown University, Department of Economics.
  2. 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), HAL halshs-00211906, HAL.
  3. Lars Nielsen, 2005. "Monotone risk aversion," Economic Theory, Springer, Springer, vol. 25(1), pages 203-215, 01.
  4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, American Finance Association, vol. 7(1), pages 77-91, 03.
  5. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, Elsevier, vol. 1(3), pages 315-329, October.
  6. James C. Cox & Vjollca Sadiraj & Bodo Vogt & Utteeyo Dasgupta, 2007. "Is There A Plausible Theory for Risky Decisions?," Experimental Economics Center Working Paper Series, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University 2007-05, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University, revised Apr 2008.
  7. Jon Eguia, 2013. "On the spatial representation of preference profiles," Economic Theory, Springer, Springer, vol. 52(1), pages 103-128, January.
  8. Dybvig, Philip H & Lippman, Steven A, 1983. "An Alternative Characterization of Decreasing Absolute Risk Aversion," Econometrica, Econometric Society, Econometric Society, vol. 51(1), pages 223-24, January.
  9. Yi-Chun Chen & Xiao Luo, 2012. "An indistinguishability result on rationalizability under general preferences," Economic Theory, Springer, Springer, vol. 51(1), pages 1-12, September.
  10. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
  11. repec:hal:journl:halshs-00211906 is not listed on IDEAS
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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, National Graduate Institute for Policy Studies 14-09, National Graduate Institute for Policy Studies.
  2. Amnon Schreiber, 2014. "Economic indices of absolute and relative riskiness," Economic Theory, Springer, Springer, vol. 56(2), pages 309-331, June.

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