Partial Moments and Negative Moments in Ordering Asymmetric Distributions

  • Grażyna Trzpiot
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


Moment ordering condition is shown to be necessary for stochastic dominance. In this paper related results of the partial moments and negative moments are presented. The condition for any degree of stochastic dominance, by ordering fractional and negative moments of the distribution, will be shown. We present the sufficient condition for restricted families of distribution functions - a class of asymmetric distributions. Additionally we present a related general measure based on fractional moments, which can be used for complete ordering the set of distributions. The condition applies generally, subject only to the requirement that the moments exist. The result rests on the fact that the negative and the fractional moments of the distribution can be interpreted as constant relative risk aversion utility function.


Utility Function Portfolio Selection Stochastic Dominance Constant Relative Risk Aversion Lorenz Dominance 
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  1. BRADLEY, M.G. and LEHMANN, D.E. (1988): Instrument Effects and Stochastic Dominance. Insurance Mathematic And Economics, 7, 185–191.MathSciNetCrossRefMATHGoogle Scholar
  2. HADAR, J. and RUSSEL, W.K. (1969): Rules for Ordering Uncertain Prospects. Amer. Economic Rev., 59, 25–34.Google Scholar
  3. HANOCH, G. and LEVY, H. (1969): The Efficiency Analysis of Choices Involving Risk. Rev. Economic Studies, 36, 335–346.MATHGoogle Scholar
  4. LEVY, H. (1992): Stochastic Dominance and Expected Utility: Survey and Analysis. Management Science, 38,4, 555–593.MATHCrossRefGoogle Scholar
  5. LEVY, H. (1996): Investment Diversification and Investment Specialization and the Assumed Holding Period. Applied Mathematical Finance, 3, 117–134.MATHGoogle Scholar
  6. MARKOWITZ, H.M. (1952): Portfolio Selection. Journal of Finance, 7, 77–91.Google Scholar
  7. OGRYCZAK, W. and RUSZCZYNSKI, A. (1999): From Stochastic Dominance to Mean Risk Models: Semideviation As Risk Measure. European Journal Of Operation Research, 116, 33–50.CrossRefMATHGoogle Scholar
  8. ROTHSCHILD, L.J. and STIGLITZ, J.E. (1970): Increasing risk I. A definition. Journal of Economic Theory, 2, 225–243.MathSciNetCrossRefGoogle Scholar
  9. TRZPIOT, G. (1998): Stochastic Dominance Under Ambiguity in Optimal Portfolio Selection: Evidence from the Warsaw Stock Exchange, Short Papers from VI Conference of the International Classification Societies, 311–315, Rome.Google Scholar
  10. TRZPIOT, G. (2002): Multicriterion analysis based on Marginal and Conditional Stochastic Dominance in Financial Analysis. In: T. Trzaskalik and J. Michnik (Eds.): Multiple Objective and Goal Programming. Physica, Heidelberg, 400–412.Google Scholar
  11. TRZPIOT, G. (2003): Advanced modeling in finance using multivalued stochastic dominance and probabilistic dominance. Journal of Economics and Management, KAUE Katowice (in appearance).Google Scholar
  12. WHITMORE, G.A. (1970): Third Degree Stochastic Dominance. Amer. Economic Rev., 60, 457–459.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 2005

Authors and Affiliations

  • Grażyna Trzpiot
    • 1
  1. 1.Department of StatisticsKatowice University of EconomicsKatowicePoland

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