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Characterizing Fractional-Degree Stochastic Dominance by Invariance Laws

Author

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  • Tiantian Mao

    (School of Management, University of Science and Technology of China, Hefei 230026, China)

  • Ruodu Wang

    (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada)

  • Lin Zhao

    (School of Business Administration, Southwestern University of Finance and Economics, Chengdu 611130, China)

Abstract

Classic notions of stochastic dominance have integer degrees. Recent studies have imposed distinct preference conditions for refinement, resulting in a range of fractional-degree stochastic dominance rules. However, preference conditions are generally not mutually exclusive, making it challenging to establish a strict criterion for rule selection. To address this, we establish fractional-degree stochastic dominance rules based exclusively on invariance laws under a general condition that is applicable to all intermediate utility sets. This approach enables practitioners to rely solely on the mutual compatibility and exclusivity of invariance properties to compare and select the appropriate rules. We illustrate the usefulness of our approach through an application to the problem of mutual fund selection.

Suggested Citation

  • Tiantian Mao & Ruodu Wang & Lin Zhao, 2026. "Characterizing Fractional-Degree Stochastic Dominance by Invariance Laws," Decision Analysis, INFORMS, vol. 23(2), pages 149-171, June.
    • Handle: RePEc:inm:ordeca:v:23:y:2026:i:2:p:149-171
    DOI: 10.1287/deca.2025.0512
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