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Stochastic Dominance: Convexity And Some Efficiency Tests

Author

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  • ANDREY LIZYAYEV

    (Erasmus School of Economics, Tinbergen Institute, Erasmus University Rotterdam, The Netherlands;
    BNG Bank, Koninginnegracht 2, 2514 AA, The Hague, The Netherlands)

Abstract

This paper points out the importance of Stochastic Dominance (SD) efficient sets being convex. We review classic convexity and efficient set characterization results on SD efficiency of a given portfolio relative to a diversified set of assets and generalize them in the following aspects. First, we propose a linear programming SSD test that is more efficient than that of Post (2003). Secondly, we expand the SSD efficiency criteria developed by Dybvig and Ross (1982) onto the Third Order Stochastic Dominance and further to Decreasing Absolute and Increasing Relative Risk Aversion Stochastic Dominance. The efficient sets for those are finite unions of convex sets.

Suggested Citation

  • Andrey Lizyayev, 2012. "Stochastic Dominance: Convexity And Some Efficiency Tests," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1-19.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:05:n:s0219024912500367
    DOI: 10.1142/S0219024912500367
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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. Leili Javanmardi & Yuri Lawryshyn, 2016. "A new rank dependent utility approach to model risk averse preferences in portfolio optimization," Annals of Operations Research, Springer, vol. 237(1), pages 161-176, February.
    3. Leili Javanmardi & Yuri Lawryshyn, 2016. "A new rank dependent utility approach to model risk averse preferences in portfolio optimization," Annals of Operations Research, Springer, vol. 237(1), pages 161-176, February.
    4. Fang, Yi & Post, Thierry, 2017. "Higher-degree stochastic dominance optimality and efficiency," European Journal of Operational Research, Elsevier, vol. 261(3), pages 984-993.

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