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Stochastic Dominance: Convexity and Some Efficiency Tests

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  • Andrey M. Lizyayev

    (Erasmus University Rotterdam)

Abstract

This paper points out the importance of Stochastic Dominance (SD) efficient sets being convex. We reviewclassic convexity and efficient set characterization results on SD efficiency of a given portfolio relative to adiversified set of assets and generalize them in the following aspects. First, we broaden the class ofindividual utilities in Rubinstein (1974) that lead to two-fund separation. Secondly, we propose a linearprogramming SSD test that is more efficient than that of Post (2003) and expand the SSD efficiency criteriadeveloped by Dybvig and Ross (1982) onto the Third Order Stochastic Dominance and further toDecreasing Absolute and Increasing Relative Risk Aversion Stochastic Dominance. The efficient sets forthose are finite unions of convex sets.

Suggested Citation

  • Andrey M. Lizyayev, 2009. "Stochastic Dominance: Convexity and Some Efficiency Tests," Tinbergen Institute Discussion Papers 09-112/2, Tinbergen Institute, revised 05 Jan 2010.
    • Handle: RePEc:tin:wpaper:20090112
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    References listed on IDEAS

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    1. Stephen A. Ross, 2005. "Mutual Fund Separation in Financial Theory—The Separating Distributions," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 10, pages 309-356, World Scientific Publishing Co. Pte. Ltd..
    2. Vijay S. Bawa, 1982. "Research Bibliography---Stochastic Dominance: A Research Bibliography," Management Science, INFORMS, vol. 28(6), pages 698-712, June.
    3. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
    4. Post, Thierry & Versijp, Philippe, 2007. "Multivariate Tests for Stochastic Dominance Efficiency of a Given Portfolio," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(2), pages 489-515, June.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
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    7. repec:bla:jfinan:v:58:y:2003:i:5:p:1905-1932 is not listed on IDEAS
    8. Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Stochastic Dominance; Convexity; Risk Aversion; Efficiency;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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