IDEAS home Printed from https://ideas.repec.org/p/pre/wpaper/201940.html
   My bibliography  Save this paper

Preferences Over Rich Sets of Random Variables: Semicontinuity in Measure versus Convexity

Author

Listed:
  • Alexander Zimper

    () (Department of Economics; University of Pretoria; postal address: Private Bag X20; Hat.eld 0028; South Africa)

  • Hirbod Assa

    () (Institute for Financial and Actuarial Mathematics and Institute for Risk and Uncertainty, University of Liverpool, Center for Doctoral Training, Chadwick Building, G62, Liverpool UK.)

Abstract

The choice of a continuity concept in decision theoretic models has behavioral meaning because it pins down how the decision maker perceives the similarity of random variables. This paper analyzes the preferences of a decision maker who perceives similarity in accordance with the topology of convergence in measure. As our main insight we show that this decision maker cannot be globally risk or ambiguity averse whenever her preferences are lower-semicontinuous and complete on a rich set of random variables. Real life decision makers who perceive the similarity of random variables in accordance with convergence in measure might thus account for violations of global convexity as observed in empirical studies. Similarly, the non-convex risk measure value-at-risk might be popular among decision makers because it represents preferences that are lower-semicontinuous in measure.

Suggested Citation

  • Alexander Zimper & Hirbod Assa, 2019. "Preferences Over Rich Sets of Random Variables: Semicontinuity in Measure versus Convexity," Working Papers 201940, University of Pretoria, Department of Economics.
  • Handle: RePEc:pre:wpaper:201940
    as

    Download full text from publisher

    File URL: http://www.up.ac.za/media/shared/61/WP/wp_2019_40.zp174567.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Dekel, Eddie, 1989. "Asset Demands without the Independence Axiom," Econometrica, Econometric Society, vol. 57(1), pages 163-169, January.
    2. Alain Chateauneuf & Michéle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 649-667, April.
    3. Freddy Delbaen, 2009. "Risk Measures For Non‐Integrable Random Variables," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 329-333, April.
    4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    5. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    6. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    7. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Similarity Perceptions; Continuous Preferences; Uncertainty; Ambiguity; Utility Representations; Risk Measures;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:pre:wpaper:201940. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Rangan Gupta). General contact details of provider: http://edirc.repec.org/data/decupza.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.