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Comparing Risks by Acceptance and Rejection

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  • Sergiu Hart

Abstract

Stochastic dominance is a partial order on risky assets ("gambles") that is based on the uniform preference--of all decision-makers in an appropriate class--for one gamble over another. We modify this requirement, first, by taking into account the status quo (given by the current wealth) and the possibility of rejecting gambles, and second, by comparing rejections that are substantive (i.e., uniform over wealth levels or over utilities). This yields two new stochastic orders: "wealth-uniform dominance" and "utility-uniform dominance." Unlike stochastic dominance, these two orders are complete: any two gambles can be compared. Moreover, they are equivalent to the orders induced by, respectively, the Aumann-Serrano index of riskiness and the Foster-Hart measure of riskiness.

Suggested Citation

  • Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617-638.
  • Handle: RePEc:ucp:jpolec:doi:10.1086/662222
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    File URL: http://dx.doi.org/10.1086/662222
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    References listed on IDEAS

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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.
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    Cited by:

    1. Riedel, Frank & Hellmann, Tobias, 2015. "The Foster-Hart measure of riskiness for general gambles," Theoretical Economics, Econometric Society, vol. 10(1), January.
    2. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2013. "Entropy and the Value of Information for Investors," American Economic Review, American Economic Association, vol. 103(1), pages 360-377, February.
    3. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Aug 2015.
    4. Foster, Dean P. & Hart, Sergiu, 2013. "A wealth-requirement axiomatization of riskiness," Theoretical Economics, Econometric Society, vol. 8(2), May.
    5. Kadan, Ohad & Liu, Fang, 2014. "Performance evaluation with high moments and disaster risk," Journal of Financial Economics, Elsevier, vol. 113(1), pages 131-155.
    6. Moti Michaeli, 2014. "Riskiness for sets of gambles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 515-547, August.
    7. Chamorro Elosua, Arritokieta & Usategui Díaz de Otalora, José María, 2013. "A Note on Risk Acceptance, Bankruptcy Avoidance and Riskiness Measures," DFAEII Working Papers DFAEII;2013-04, University of the Basque Country - Department of Foundations of Economic Analysis II.
    8. Menegatti, Mario, 2015. "New results on high-order risk changes," European Journal of Operational Research, Elsevier, vol. 243(2), pages 678-681.
    9. Schreiber, Amnon, 2015. "A note on Aumann and Serrano’s index of riskiness," Economics Letters, Elsevier, vol. 131(C), pages 9-11.
    10. 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.
    11. Schnytzer, Adi & Westreich, Sara, 2013. "A global index of riskiness," Economics Letters, Elsevier, vol. 118(3), pages 493-496.
    12. Cabrales, Antonio & Gossner, Olivier & Serrano, Roberto, 2017. "A normalized value for information purchases," Journal of Economic Theory, Elsevier, vol. 170(C), pages 266-288.
    13. Bali, Turan G. & Cakici, Nusret & Chabi-Yo, Fousseni, 2015. "A new approach to measuring riskiness in the equity market: Implications for the risk premium," Journal of Banking & Finance, Elsevier, vol. 57(C), pages 101-117.
    14. Anand, Abhinav & Li, Tiantian & Kurosaki, Tetsuo & Kim, Young Shin, 2016. "Foster–Hart optimal portfolios," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 117-130.
    15. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Working Papers 2012-13, Brown University, Department of Economics.
    16. Klaas Schulze, 2015. "General dual measures of riskiness," Theory and Decision, Springer, vol. 78(2), pages 289-304, February.
    17. repec:eee:ecolet:v:164:y:2018:i:c:p:62-64 is not listed on IDEAS
    18. Kent Smetters & Xingtan Zhang, 2013. "A Sharper Ratio: A General Measure for Correctly Ranking Non-Normal Investment Risks," NBER Working Papers 19500, National Bureau of Economic Research, Inc.
    19. Menegatti, Mario, 2014. "New results on the relationship among risk aversion, prudence and temperance," European Journal of Operational Research, Elsevier, vol. 232(3), pages 613-617.
    20. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2011. "Entropy and the value of information for investors," Working Papers halshs-00648884, HAL.
    21. Amnon Schreiber, 2012. "An Economic Index of Relative Riskiness," Discussion Paper Series dp597, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

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