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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

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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Similarity Perceptions; Continuous Preferences; Uncertainty; Ambiguity; Utility Representations; Risk Measures;
    All these keywords.

    JEL classification:

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

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