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Fractional stochastic dominance in rank-dependent utility and cumulative prospect theory

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  • Mao, Tiantian
  • Wang, Ruodu

Abstract

Two notions of fractional stochastic dominance (SD) were recently proposed by Müller et al. (2017) and Huang et al. (2020) based on mean-reducing spreads and the coefficient of absolute risk aversion, respectively. We formulate a general class of fractional SD generated by a convex transform, which includes those built from absolute or relative risk aversion as special cases, and this serves as a convenient technical tool for construction of new notions of fractional SD. We obtain equivalent conditions for a preference modeled by rank-dependent utility or cumulative prospect theory to be consistent with each notion of fractional SD. Furthermore, we provide an empirical estimator for the parameters in fractional SD relationships, and we illustrate this with a financial data analysis.

Suggested Citation

  • Mao, Tiantian & Wang, Ruodu, 2022. "Fractional stochastic dominance in rank-dependent utility and cumulative prospect theory," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    • Handle: RePEc:eee:mateco:v:103:y:2022:i:c:s0304406822000921
    DOI: 10.1016/j.jmateco.2022.102766
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    References listed on IDEAS

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    1. Alfred Müller & Marco Scarsini & Ilia Tsetlin & Robert L. Winkler, 2025. "Multivariate Almost Stochastic Dominance: Transfer Characterizations and Sufficient Conditions Under Dependence Uncertainty," Operations Research, INFORMS, vol. 73(2), pages 879-893, March.
    2. Ehsan Azmoodeh & Ozan Hur, 2023. "Generalized Families of Fractional Stochastic Dominance," Papers 2307.08651, arXiv.org, revised Feb 2025.
    3. Ruodu Wang & Qinyu Wu, 2024. "Prudence and higher-order risk attitudes in the rank-dependent utility model," Papers 2412.15350, arXiv.org, revised Sep 2025.
    4. Christian Laudag'e & Felix-Benedikt Liebrich, 2025. "When risk defies order: On the limits of fractional stochastic dominance," Papers 2509.24747, arXiv.org.
    5. Wang, Ruodu & Wu, Qinyu, 2025. "Prudence and higher-order risk attitudes in the rank-dependent utility model," Journal of Mathematical Economics, Elsevier, vol. 121(C).

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