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Sufficient conditions of stochastic dominance for general transformations and its application in option strategy

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  • Gao, Jianwei
  • Zhao, Feng
  • Gu, Yundong

Abstract

A counterexample is presented to show that the sufficient condition for one transformation dominating another by the second degree stochastic dominance, proposed by Theorem 5 of Levy (Stochastic dominance and expected utility: Survey and analysis, 1992), does not hold. Then, by restricting the monotone property of the dominating transformation, a revised exact sufficient condition for one transformation dominating another is given. Next, the stochastic dominance criteria, proposed by Meyer (Stochastic dominance and transformations of random variables, 1989) and developed by Levy (1992), are extended to the most general transformations. Moreover, such criteria are further generalized to transformations on discrete random variables. Finally, the authors employ this method to analyze the transformations resulting from holding a stock with the corresponding call option.

Suggested Citation

  • Gao, Jianwei & Zhao, Feng & Gu, Yundong, 2018. "Sufficient conditions of stochastic dominance for general transformations and its application in option strategy," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 12, pages 1-15.
    • Handle: RePEc:zbw:ifweej:20181
    DOI: 10.5018/economics-ejournal.ja.2018-1
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    References listed on IDEAS

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    1. Satya R. Chakravarty & Claudio Zoli, 2019. "Stochastic Dominance Relations for Integer Variables," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 211-222, Springer.
    2. Cheng, Hsueh-Cheng & Magill, Michael J P & Shafer, Wayne J, 1987. "Some Results on Comparative Statics under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(2), pages 493-507, June.
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    More about this item

    Keywords

    stochastic dominance; transformation; utility theory; option strategy;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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