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Consistent modeling of risk averse behavior with spectral risk measures: Wächter/Mazzoni revisited

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  • Brandtner, Mario
  • Kürsten, Wolfgang

Abstract

Wächter and Mazzoni (2013) (W/M) have proposed a procedure to consistently link traditional expected utility (EU)-theory with modern spectral risk measures (SRMs). They construct a corresponding W/M-risk measure which induces the same preference ordering as the decision maker’s initial utility function does. In this note, we revisit W/M’s procedure and show that it violates the axiomatic foundation of the underlying decision rules: Within the general part of the procedure that builds on an auxiliary equivalent probability measure, the emerging W/M-risk measure does not satisfy the axiomatic properties of SRMs. The specific part of the procedure that singles out a preferred equivalent probability measure links two decision rules of which neither does the initial one respect the axioms of EU-theory, nor is the emerging one in line with the SRM-axioms.

Suggested Citation

  • Brandtner, Mario & Kürsten, Wolfgang, 2017. "Consistent modeling of risk averse behavior with spectral risk measures: Wächter/Mazzoni revisited," European Journal of Operational Research, Elsevier, vol. 259(1), pages 394-399.
    • Handle: RePEc:eee:ejores:v:259:y:2017:i:1:p:394-399
    DOI: 10.1016/j.ejor.2016.12.027
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    References listed on IDEAS

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    1. Wächter, Hans Peter & Mazzoni, Thomas, 2013. "Consistent modeling of risk averse behavior with spectral risk measures," European Journal of Operational Research, Elsevier, vol. 229(2), pages 487-495.
    2. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    3. Alexandre Adam & Mohamed Houkari & Jean-Paul Laurent, 2008. "Spectral risk measures and portfolio selection," Post-Print hal-03676385, HAL.
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    5. Newbery, David, 1970. "A theorem on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 264-266, September.
    6. Brandtner, Mario & Kürsten, Wolfgang, 2015. "Decision making with Expected Shortfall and spectral risk measures: The problem of comparative risk aversion," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 268-280.
    7. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
    8. Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "Comparative Analyses of Expected Shortfall and Value-at-Risk (2): Expected Utility Maximization and Tail Risk," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(2), pages 95-115, April.
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    Cited by:

    1. Takashi Kato, 2017. "Asymptotic Analysis for Spectral Risk Measures Parameterized by Confidence Level," Papers 1711.07335, arXiv.org.
    2. Adam, Lukáš & Branda, Martin, 2021. "Risk-aversion in data envelopment analysis models with diversification," Omega, Elsevier, vol. 102(C).

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