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Probabilistic risk aversion for generalized rank-dependent functions

Author

Listed:
  • Ruodu Wang

    (University of Waterloo)

  • Qinyu Wu

    (University of Waterloo)

Abstract

Probabilistic risk aversion, defined through quasi-convexity in probabilistic mixtures, is a common useful property in decision analysis. We study a general class of non-monotone mappings, called the generalized rank-dependent functions, which includes the preference models of expected utilities, dual utilities, and rank-dependent utilities as special cases, as well as signed Choquet functions used in risk management. Our results fully characterize probabilistic risk aversion for generalized rank-dependent functions: This property is determined by the distortion function, which is precisely one of the two cases: those that are convex and those that correspond to scaled quantile-spread mixtures. Our result also leads to seven equivalent conditions for quasi-convexity in probabilistic mixtures of dual utilities and signed Choquet functions. As a consequence, although probabilistic risk aversion is quite different from the classic notion of strong risk aversion for generalized rank-dependent functions, these two notions coincide for dual utilities under an additional continuity assumption.

Suggested Citation

  • Ruodu Wang & Qinyu Wu, 2025. "Probabilistic risk aversion for generalized rank-dependent functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(3), pages 1055-1082, May.
    • Handle: RePEc:spr:joecth:v:79:y:2025:i:3:d:10.1007_s00199-024-01610-8
    DOI: 10.1007/s00199-024-01610-8
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    More about this item

    Keywords

    Quasi-convexity; Risk aversion; Signed Choquet functions; Rank-dependent utilities; Probabilistic mixtures;
    All these keywords.

    JEL classification:

    • D30 - Microeconomics - - Distribution - - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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