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Relative risk aversion, relative prudence and comparative statics under uncertainty: The case of (μ, σ)‐preferences

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  • Thomas Eichner
  • Andreas Wagener

Abstract

From the expected‐utility approach, relative risk aversion being smaller than one and relative prudence being smaller than two emerge as preference restrictions that fully determine the optimal responses of decisions under uncertainty to certain shifts in probability distributions. We characterize the magnitudes of relative risk aversion and relative prudence in terms of the two‐parameter, mean‐standard deviation approach. We demonstrate that this characterization is instrumental in obtaining comparative static results in the two‐parameter setting. We further relate our findings to the results in the expected‐utility framework.

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  • Thomas Eichner & Andreas Wagener, 2004. "Relative risk aversion, relative prudence and comparative statics under uncertainty: The case of (μ, σ)‐preferences," Bulletin of Economic Research, Wiley Blackwell, vol. 56(2), pages 159-170, April.
    • Handle: RePEc:bla:buecrs:v:56:y:2004:i:2:p:159-170
    DOI: 10.1111/j.1467-8586.2004.00194.x
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    2. Broll, Udo & Eckwert, Bernhard & Eickhoff, Andreas, 2011. "Transparency in the banking sector," Dresden Discussion Paper Series in Economics 05/11, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    3. Donatella Baiardi & Marco Magnani & Mario Menegatti, 2020. "The theory of precautionary saving: an overview of recent developments," Review of Economics of the Household, Springer, vol. 18(2), pages 513-542, June.
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    5. Thomas Eichner & Andreas Wagener, 2005. "Notes and Comments: Measures of risk attitude: correspondences between mean-variance and expected-utility approaches," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 28(1), pages 53-65, June.
    6. Subhadip Mukherjee & Soumyatanu Mukherjee & Tapas Mishra & Udo Broll, 2019. "Export investment under uncertainty: a mean-variance decision analysis for Indian manufacturing exporters," Discussion Papers 2019-18, University of Nottingham, GEP.
    7. Xu Guo & Andreas Wagener & Wing-Keung Wong & Lixing Zhu, 2018. "The two-moment decision model with additive risks," Risk Management, Palgrave Macmillan, vol. 20(1), pages 77-94, February.
    8. Jingyuan Li, 2012. "Precautionary saving in the presence of labor income and interest rate risks," Journal of Economics, Springer, vol. 106(3), pages 251-266, July.
    9. repec:ebl:ecbull:v:4:y:2005:i:1:p:1-8 is not listed on IDEAS
    10. Bonilla, Claudio A. & Ruiz, Jose L., 2014. "Insurance demand and first order risk increases under (μ,σ)-preferences," Finance Research Letters, Elsevier, vol. 11(3), pages 219-223.
    11. Broll, Udo & Eckwert, Bernhard & Eickhoff, Andreas, 2012. "Financial intermediation and endogenous risk in the banking sector," Economic Modelling, Elsevier, vol. 29(5), pages 1618-1622.
    12. Vergara, Marcos & Bonilla, Claudio A., 2021. "Precautionary saving in mean-variance models and different sources of risk," Economic Modelling, Elsevier, vol. 98(C), pages 280-289.
    13. Tao Yuqing & Cheng Wen & Zou Sijie, 2018. "Priority Setting in Health Care with Disease and Treatment Risks," Journal of Systems Science and Information, De Gruyter, vol. 6(6), pages 552-562, December.
    14. Fatma Lajeri-Chaherli, 2016. "On The Concavity And Quasiconcavity Properties Of ( Σ , Μ ) Utility Functions," Bulletin of Economic Research, Wiley Blackwell, vol. 68(3), pages 287-296, April.
    15. Subhadip Mukherjee & Soumyatanu Mukherjee & Tapas Mishra & Udo Broll & Mamata Parhi, 2021. "Spot exchange rate volatility, uncertain policies and export investment decision of firms: a mean-variance decision approach," The European Journal of Finance, Taylor & Francis Journals, vol. 27(8), pages 752-773, May.
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    17. Broll, Udo & Egozcue, Martín & Wong, Wing-Keung, 2009. "Prospect theory and two moment model: the firm under price uncertainty," Dresden Discussion Paper Series in Economics 01/09, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
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    20. Broll, Udo & Roldán-Ponce, Antonio & Wahl, Jack E., 2012. "Regional investment under uncertain costs of location," Dresden Discussion Paper Series in Economics 01/12, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.

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