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Higher-Order Risk Measure and (Higher-Order) Stochastic Dominance

Author

Listed:
  • Niu, Cuizhen
  • Wong, Wing-Keung
  • Xu, Qunfang

Abstract

This paper extends the theory between Kappa ratio and stochastic dominance (SD) and risk-seeking SD (RSD) by establishing several relationships between first- and higher-order risk measures and (higher-order) SD and RSD. We first show the sufficient relationship between the (n+1)-order SD and the n-order Kappa ratio. We then find that, in general, the necessary relationship between SD/RSD and the Kappa ratio cannot be established. Thereafter, we find that when the variables being compared belong to the same location-scale family or the same linear combination of location-scale families, we can get the necessary relationships between the (n+1)-order SD with the n-order Kappa ratio when we impose some conditions on the means. Our findings enable academics and practitioners to draw better decision in their analysis.

Suggested Citation

  • Niu, Cuizhen & Wong, Wing-Keung & Xu, Qunfang, 2017. "Higher-Order Risk Measure and (Higher-Order) Stochastic Dominance," MPRA Paper 75948, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:75948
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    File URL: https://mpra.ub.uni-muenchen.de/75948/1/MPRA_paper_75948.pdf
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    References listed on IDEAS

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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Stochastic Dominance; Kappa ratio; Omega Ratio; Sortino ratio; mean-risk analysis; risk aversion; risk seeking;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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