IDEAS home Printed from https://ideas.repec.org/p/zbw/ifwedp/201649.html
   My bibliography  Save this paper

A new approach of stochastic dominance for ranking transformations on the discrete random variable

Author

Listed:
  • Gao, Jianwei
  • Zhao, Feng

Abstract

This paper develops some new stochastic dominance (SD) rules for ranking transformations on a random variable, which is the first time to study ranking approach for transformations on the discrete framework. By using the expected utility theory, the authors first present a sufficient condition for general transformations by first degree SD (FSD), and further develop it into the necessary and sufficient condition for the monotonic transformations. For the second degree SD (SSD) case, the authors divide the monotonic transformations into increasing and decreasing ones, and respectively derive the necessary and sufficient conditions for the two situations. For two different discrete random variables with the same possible states, they obtain the sufficient and necessary condition for FSD and SSD, respectively. The feature of the new SD rules is that each FSD condition is represented by the transformation functions and each SSD condition is characterized by the transformation functions and the probability distributions of the random variable. This is different from the existing SD approach where they are described by cumulative distribution functions. In this way, the authors construct a new theoretical paradigm for transformations on the discrete random variable. Finally, a numerical example is provided to show the effectiveness of the new SD rules.

Suggested Citation

  • Gao, Jianwei & Zhao, Feng, 2016. "A new approach of stochastic dominance for ranking transformations on the discrete random variable," Economics Discussion Papers 2016-49, Kiel Institute for the World Economy (IfW Kiel).
    • Handle: RePEc:zbw:ifwedp:201649
    as

    Download full text from publisher

    File URL: http://www.economics-ejournal.org/economics/discussionpapers/2016-49
    Download Restriction: no
    File URL: https://www.econstor.eu/bitstream/10419/148421/1/875106048.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Larry Y. Tzeng & Rachel J. Huang & Pai-Ta Shih, 2013. "Revisiting Almost Second-Degree Stochastic Dominance," Management Science, INFORMS, vol. 59(5), pages 1250-1254, May.
    2. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    3. Wang, Lijian & Béland, Daniel & Zhang, Sifeng, 2014. "Pension financing in China: Is there a looming crisis?," China Economic Review, Elsevier, vol. 30(C), pages 143-154.
    4. Chiu, W.Henry, 2005. "Degree of downside risk aversion and self-protection," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 93-101, February.
    5. Ilia Tsetlin & Robert L. Winkler & Rachel J. Huang & Larry Y. Tzeng, 2015. "Generalized Almost Stochastic Dominance," Operations Research, INFORMS, vol. 63(2), pages 363-377, April.
    6. Li, Jingyuan, 2009. "Comparative higher-degree Ross risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 333-336, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gao, Jianwei & Zhao, Feng, 2017. "A new approach of stochastic dominance for ranking transformations on the discrete random variable," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 11, pages 1-23.
    2. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2016. "Almost stochastic dominance for risk averters and risk seeker," Finance Research Letters, Elsevier, vol. 19(C), pages 15-21.
    3. Francesco Cesarone & Justo Puerto, 2024. "New approximate stochastic dominance approaches for Enhanced Indexation models," Papers 2401.12669, arXiv.org.
    4. Bruni, Renato & Cesarone, Francesco & Scozzari, Andrea & Tardella, Fabio, 2017. "On exact and approximate stochastic dominance strategies for portfolio selection," European Journal of Operational Research, Elsevier, vol. 259(1), pages 322-329.
    5. Yi-Chieh Huang & Kamhon Kan & Larry Y. Tzeng & Kili C. Wang, 2021. "Estimating the Critical Parameter in Almost Stochastic Dominance from Insurance Deductibles," Management Science, INFORMS, vol. 67(8), pages 4742-4755, August.
    6. Hermann Jahnke & Jan Thomas Martini & Tobias Wiens, 2019. "Price limits under incomplete preference information based on almost stochastic dominance," Business Research, Springer;German Academic Association for Business Research, vol. 12(1), pages 241-269, April.
    7. Chin Hon Tan & Chunling Luo, 2017. "Clear Preferences Under Partial Distribution Information," Decision Analysis, INFORMS, vol. 14(1), pages 65-73, March.
    8. Lee, Yung-Tsung & Kung, Ko-Lun & Liu, I-Chien, 2018. "Profitability and risk profile of reverse mortgages: A cross-system and cross-plan comparison," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 255-266.
    9. Jow-Ran Chang & Wei-Han Liu & Mao-Wei Hung, 2019. "Revisiting generalized almost stochastic dominance," Annals of Operations Research, Springer, vol. 281(1), pages 175-192, October.
    10. Tommaso Lando & Lucio Bertoli-Barsotti, 2019. "Distorted stochastic dominance: a generalized family of stochastic orders," Papers 1909.04767, arXiv.org.
    11. Xu, Guo & Wing-Keung, Wong & Lixing, Zhu, 2013. "Almost Stochastic Dominance for Risk-Averse and Risk-Seeking Investors," MPRA Paper 51744, University Library of Munich, Germany.
    12. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," JRFM, MDPI, vol. 11(1), pages 1-29, March.
    13. Zhao, Kena & Ng, Tsan Sheng & Tan, Chin Hon & Pang, Chee Khiang, 2021. "An almost robust model for minimizing disruption exposures in supply systems," European Journal of Operational Research, Elsevier, vol. 295(2), pages 547-559.
    14. Lando, Tommaso & Bertoli-Barsotti, Lucio, 2020. "Distorted stochastic dominance: A generalized family of stochastic orders," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 132-139.
    15. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2013. "Almost Stochastic Dominance and Moments," MPRA Paper 49274, University Library of Munich, Germany.
    16. Liqun Liu & Nicolas Treich, 2021. "Optimality of winner-take-all contests: the role of attitudes toward risk," Journal of Risk and Uncertainty, Springer, vol. 63(1), pages 1-25, August.
    17. Caporin, Massimiliano & Costola, Michele & Jannin, Gregory & Maillet, Bertrand, 2018. "“On the (Ab)use of Omega?”," Journal of Empirical Finance, Elsevier, vol. 46(C), pages 11-33.
    18. Chen, Tzu-Ying & Tsai, An-Mei & Tzeng, Larry Y., 2022. "Revisiting almost marginal conditional stochastic dominance," The Quarterly Review of Economics and Finance, Elsevier, vol. 85(C), pages 260-269.
    19. Tzu-Ying Chen & Yi-Hsin Elsa Hsu & Rachel J. Huang & Larry Y. Tzeng, 2021. "Making socioeconomic health inequality comparisons when health concentration curves intersect," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 875-899, November.
    20. Chang, C-L. & McAleer, M.J. & Wong, W.-K., 2016. "Management Science, Economics and Finance: A Connection," Econometric Institute Research Papers EI2016-26, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

    More about this item

    Keywords

    stochastic dominance; transformation; utility theory; insurance;
    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
    • G1 - Financial Economics - - General Financial Markets

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:ifwedp:201649. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/iwkiede.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.