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Further Developments on Stochastic Dominance for Different Classes of Infinite-mean Distributions

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Listed:
  • Keyi Zeng
  • Zhenfeng Zou
  • Yuting Su
  • Taizhong Hu

Abstract

In recent years, stochastic dominance for independent and identically distributed (iid) infinite-mean random variables has received considerable attention. The literature has identified several classes of distributions of nonnegative random variables that encompass many common heavy-tailed distributions. A key result demonstrates that the weighted sum of iid random variables from these classes is stochastically larger than any individual random variable in the sense of the first-order stochastic dominance. This paper systematically investigates the properties and inclusion relationships among these distribution classes, and extends some existing results to more practical scenarios. Furthermore, we analyze the case where each random variable follows a compound binomial distribution, establishing necessary and sufficient conditions for the preservation of the aforementioned stochastic dominance relation.

Suggested Citation

  • Keyi Zeng & Zhenfeng Zou & Yuting Su & Taizhong Hu, 2025. "Further Developments on Stochastic Dominance for Different Classes of Infinite-mean Distributions," Papers 2511.00764, arXiv.org.
    • Handle: RePEc:arx:papers:2511.00764
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    References listed on IDEAS

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    1. Yuyu Chen & Seva Shneer, 2024. "Risk aggregation and stochastic dominance for a class of heavy-tailed distributions," Papers 2408.15033, arXiv.org, revised May 2025.
    2. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    3. Yuri Imamura & Takashi Kato, 2025. "A Note on Subadditivity of Value at Risks (VaRs): A New Connection to Comonotonicity," Papers 2509.12558, arXiv.org, revised Oct 2025.
    4. Yuyu Chen & Paul Embrechts & Ruodu Wang, 2025. "Technical Note—An Unexpected Stochastic Dominance: Pareto Distributions, Dependence, and Diversification," Operations Research, INFORMS, vol. 73(3), pages 1336-1344, May.
    5. L'eonard Vincent, 2025. "Diversification and Stochastic Dominance: When All Eggs Are Better Put in One Basket," Papers 2507.16265, arXiv.org, revised Aug 2025.
    6. Yuyu Chen & Taizhong Hu & Ruodu Wang & Zhenfeng Zou, 2024. "Diversification for infinite-mean Pareto models without risk aversion," Papers 2404.18467, arXiv.org, revised Feb 2025.
    7. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    8. Yuyu Chen & Taizhong Hu & Seva Shneer & Zhenfeng Zou, 2025. "Stochastic dominance for linear combinations of infinite-mean risks," Papers 2505.01739, arXiv.org.
    9. Chen, Yuyu & Hu, Taizhong & Wang, Ruodu & Zou, Zhenfeng, 2025. "Diversification for infinite-mean Pareto models without risk aversion," European Journal of Operational Research, Elsevier, vol. 323(1), pages 341-350.
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