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Concave/convex weighting and utility functions for risk: A new light on classical theorems

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  • Wakker, Peter P.
  • Yang, Jingni

Abstract

This paper analyzes concave and convex utility and probability distortion functions for decision under risk (law-invariant functionals). We characterize concave utility for virtually all existing models, and concave/convex probability distortion functions for rank-dependent utility and prospect theory in complete generality, through an appealing and well-known condition (convexity of preference, i.e., quasiconcavity of the functional). Unlike preceding results, we do not need to presuppose any continuity, let be differentiability.

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  • Wakker, Peter P. & Yang, Jingni, 2021. "Concave/convex weighting and utility functions for risk: A new light on classical theorems," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 429-435.
    • Handle: RePEc:eee:insuma:v:100:y:2021:i:c:p:429-435
    DOI: 10.1016/j.insmatheco.2021.07.002
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    Cited by:

    1. Felix-Benedikt Liebrich & Cosimo Munari, 2022. "Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity," Mathematics and Financial Economics, Springer, volume 16, number 2, February.
    2. Giulio Principi & Peter P. Wakker & Ruodu Wang, 2023. "Anticomonotonicity for Preference Axioms: The Natural Counterpart to Comonotonicity," Papers 2307.08542, arXiv.org, revised Dec 2024.
    3. Aniruddha Ghosh & M. Ali Khan & Metin Uyanık, 2023. "Continuity postulates and solvability axioms in economic theory and in mathematical psychology: a consolidation of the theory of individual choice," Theory and Decision, Springer, vol. 94(2), pages 189-210, February.
    4. Ruodu Wang & Qinyu Wu, 2022. "Probabilistic risk aversion for generalized rank-dependent functions," Papers 2209.03425, arXiv.org, revised Sep 2024.

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    More about this item

    Keywords

    Convex preferences; Quasiconcave utility; Risk aversion; Rank-dependent utility;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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