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Mean Variance Vulnerability

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  • Thomas Eichner

    () (Department of Economics, University of Bielefeld, D-33615 Bielefeld, Germany)

Abstract

This paper transfers the concept of Gollier and Pratt's (Gollier, C., J. W. Pratt. 1996. Risk vulnerability and the tempering effect of background risk. Econometrica 64 1109-1123) risk vulnerability into mean variance preferences. Risk vulnerability is shown to be equivalent to the slope of the mean variance indifference curve being decreasing in mean and increasing in variance. Next, we introduce the notion of mean variance vulnerability to link the concepts of decreasing absolute risk aversion, risk vulnerability, properness, and standardness. All of the abovementioned concepts are characterized in terms of mean variance indifference curve properties and in terms of absolute risk measures.

Suggested Citation

  • Thomas Eichner, 2008. "Mean Variance Vulnerability," Management Science, INFORMS, vol. 54(3), pages 586-593, March.
  • Handle: RePEc:inm:ormnsc:v:54:y:2008:i:3:p:586-593
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    File URL: http://dx.doi.org/10.1287/mnsc.1070.0772
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Bontems, Philippe & Nauges, Céline, 2017. "Production choices with water markets: The role of initial allocations and forward trading," TSE Working Papers 17-812, Toulouse School of Economics (TSE).
    2. De Pinto, Alessandro & Robertson, Richard D. & Obiri, Beatrice Darko, 2013. "Adoption of climate change mitigation practices by risk-averse farmers in the Ashanti Region, Ghana," Ecological Economics, Elsevier, vol. 86(C), pages 47-54.
    3. 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.
    4. repec:bla:jrinsu:v:85:y:2018:i:2:p:397-430 is not listed on IDEAS
    5. Malevergne, Y. & Rey, B., 2009. "On cross-risk vulnerability," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 224-229, October.
    6. Thomas Eichner & Daniel Weinreich, 2015. "Welfare stigma and risk taking in the welfare state," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 319-348, February.
    7. Christian Gollier & Miles S. Kimball, 2018. "Toward a Systematic Approach to the Economic Effects of Risk: Characterizing Utility Functions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(2), pages 397-430, June.
    8. Jiang, Chonghui & Ma, Yongkai & An, Yunbi, 2010. "An analysis of portfolio selection with background risk," Journal of Banking & Finance, Elsevier, vol. 34(12), pages 3055-3060, December.
    9. Ebert, Sebastian & Wiesen, Daniel, 2009. "An experimental methodology testing for prudence and third-order preferences," Bonn Econ Discussion Papers 21/2009, University of Bonn, Bonn Graduate School of Economics (BGSE).
    10. Eichner, Thomas & Wagener, Andreas, 2012. "Tempering effects of (dependent) background risks: A mean-variance analysis of portfolio selection," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 422-430.
    11. Xu, Guo & Wing-Keung, Wong & Lixing, Zhu, 2013. "Comparisons and Characterizations of the Mean-Variance, Mean-VaR, Mean-CVaR Models for Portfolio Selection With Background Risk," MPRA Paper 51827, University Library of Munich, Germany.
    12. Guo, Xu & Wagener, Andreas & Wong, Wing-Keung & Zhu, Lixing, 2017. "The Two-Moment Decision Model with Additive Risks," MPRA Paper 77625, University Library of Munich, Germany.
    13. Weinreich, Daniel, 2013. "The perception of distributive fairness and optimal taxation under uncertainty," MPRA Paper 48912, University Library of Munich, Germany.
    14. Eichner, Thomas, 2011. "Portfolio selection and duality under mean variance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 146-152, January.
    15. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2013. "An analysis of portfolio selection with multiplicative background risk," MPRA Paper 51331, University Library of Munich, Germany.

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    Keywords

    mean; variance; vulnerability; properness; standardness;

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