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

Alexander Zimper and Hirbod Assa ()
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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.

No 201940, Working Papers from University of Pretoria, Department of Economics

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.

Keywords: Similarity Perceptions; Continuous Preferences; Uncertainty; Ambiguity; Utility Representations; Risk Measures (search for similar items in EconPapers)
JEL-codes: D81 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-rmg and nep-upt
Date: 2019-05
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