Probabilistic risk aversion for generalized rank-dependent functions

Ruodu Wang () and Qinyu Wu ()
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Ruodu Wang: University of Waterloo
Qinyu Wu: University of Waterloo

Economic Theory, 2025, vol. 79, issue 3, No 9, 1055-1082

Abstract: 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.

Keywords: Quasi-convexity; Risk aversion; Signed Choquet functions; Rank-dependent utilities; Probabilistic mixtures (search for similar items in EconPapers)
JEL-codes: D30 D70 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00199-024-01610-8

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