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Orderings and Probability Functionals Consistent with Preferences

Author

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  • 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.

Suggested Citation

  • Sergio Ortobelli & Svetlozar Rachev & Haim Shalit & Frank Fabozzi, 2009. "Orderings and Probability Functionals Consistent with Preferences," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 81-102.
    • Handle: RePEc:taf:apmtfi:v:16:y:2009:i:1:p:81-102
    DOI: 10.1080/13504860802327180
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Malavasi, Matteo & Ortobelli Lozza, Sergio & Trück, Stefan, 2021. "Second order of stochastic dominance efficiency vs mean variance efficiency," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1192-1206.
    2. Sergio Ortobelli & Noureddine Kouaissah & Tomáš Tichý, 2017. "On the impact of conditional expectation estimators in portfolio theory," Computational Management Science, Springer, vol. 14(4), pages 535-557, October.
    3. Raymond H. Chan & Ephraim Clark & Xu Guo & Wing-Keung Wong, 2020. "New development on the third-order stochastic dominance for risk-averse and risk-seeking investors with application in risk management," Risk Management, Palgrave Macmillan, vol. 22(2), pages 108-132, June.
    4. 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.
    5. Ran Ji & Miguel A. Lejeune & Srinivas Y. Prasad, 2017. "Properties, formulations, and algorithms for portfolio optimization using Mean-Gini criteria," Annals of Operations Research, Springer, vol. 248(1), pages 305-343, January.
    6. Sergio Ortobelli Lozza & Tommaso Lando & Filomena Petronio & Tomáš Tichý, 2016. "Asymptotic Multivariate Dominance: A Financial Application," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1097-1115, December.
    7. Iosif Pinelis, 2014. "An Optimal Three-Way Stable and Monotonic Spectrum of Bounds on Quantiles: A Spectrum of Coherent Measures of Financial Risk and Economic Inequality," Risks, MDPI, vol. 2(3), pages 1-44, September.
    8. Rosella Giacometti & Sergio Ortobelli & Tomáš Tichý, 2015. "Portfolio Selection with Uncertainty Measures Consistent with Additive Shifts," Prague Economic Papers, Prague University of Economics and Business, vol. 2015(1), pages 3-16.
    9. Alain Ruttiens, 2013. "Portfolio Risk Measures: The Time’s Arrow Matters," Computational Economics, Springer;Society for Computational Economics, vol. 41(3), pages 407-424, March.

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    More about this item

    Keywords

    G11; C44; C61;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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