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Orderings and Probability Functionals Consistent with Preferences

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Author Info

  • Sergio Ortobelli
  • Svetlozar Rachev
  • Haim Shalit
  • Frank Fabozzi

Abstract

This paper unifies the classical theory of stochastic dominance and investor preferences with the recent literature on risk measures applied to the choice problem faced by investors. First, we summarize the main stochastic dominance rules used in the finance literature. Then we discuss the connection with the theory of integral stochastic orders and we introduce orderings consistent with investors' preferences. Thus, we classify them, distinguishing several categories of orderings associated with different classes of investors. Finally, we show how we can use risk measures and orderings consistent with some preferences to determine the investors' optimal choices.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 16 (2009)
Issue (Month): 1 ()
Pages: 81-102

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Handle: RePEc:taf:apmtfi:v:16:y:2009:i:1:p:81-102

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Related research

Keywords: G11; C44; C61;

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References

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  1. Fishburn, Peter C., 1976. "Continua of stochastic dominance relations for bounded probability distributions," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 295-311, December.
  2. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2004. "Portfolio Selection with Monotone Mean-Variance Preferences," Carlo Alberto Notebooks 6, Collegio Carlo Alberto, revised 2007.
  3. Svetlozar Rachev & Sergio Ortobelli & Stoyan Stoyanov & Frank J. Fabozzi & Almira Biglova, 2008. "Desirable Properties Of An Ideal Risk Measure In Portfolio Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 19-54.
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Citations

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Cited by:
  1. Alain Ruttiens, 2013. "Portfolio Risk Measures: The Time’s Arrow Matters," Computational Economics, Society for Computational Economics, vol. 41(3), pages 407-424, March.
  2. Iosif Pinelis, 2013. "An optimal three-way stable and monotonic spectrum of bounds on quantiles: a spectrum of coherent measures of financial risk and economic inequality," Papers 1310.6025, arXiv.org.

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