IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2505.01739.html
   My bibliography  Save this paper

Stochastic dominance for linear combinations of infinite-mean risks

Author

Listed:
  • Yuyu Chen
  • Taizhong Hu
  • Seva Shneer
  • Zhenfeng Zou

Abstract

In this paper, we establish a sufficient condition to compare linear combinations of independent and identically distributed (iid) infinite-mean random variables under usual stochastic order. We introduce a new class of distributions that includes many commonly used heavy-tailed distributions and show that within this class, a linear combination of random variables is stochastically larger when its weight vector is smaller in the sense of majorization order. We proceed to study the case where each random variable is a compound Poisson sum and demonstrate that if the stochastic dominance relation holds, the summand of the compound Poisson sum belongs to our new class of distributions. Additional discussions are presented for stable distributions.

Suggested Citation

  • Yuyu Chen & Taizhong Hu & Seva Shneer & Zhenfeng Zou, 2025. "Stochastic dominance for linear combinations of infinite-mean risks," Papers 2505.01739, arXiv.org.
    • Handle: RePEc:arx:papers:2505.01739
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2505.01739
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rafal Weron, 1996. "Correction to: "On the Chambers-Mallows-Stuck Method for Simulating Skewed Stable Random Variables"," HSC Research Reports HSC/96/01, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    2. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, March.
    3. Ibragimov, Rustam & Jaffee, Dwight & Walden, Johan, 2011. "Diversification disasters," Journal of Financial Economics, Elsevier, vol. 99(2), pages 333-348, February.
    4. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
    5. 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.
    6. Rustam Ibragimov & Johan Walden, 2010. "Optimal Bundling Strategies Under Heavy-Tailed Valuations," Management Science, INFORMS, vol. 56(11), pages 1963-1976, November.
    7. Yuyu Chen & Paul Embrechts & Ruodu Wang, 2022. "An unexpected stochastic dominance: Pareto distributions, dependence, and diversification," Papers 2208.08471, arXiv.org, revised Mar 2024.
    8. Zhang, Yiying & Cheung, Ka Chun, 2020. "On the increasing convex order of generalized aggregation of dependent random variables," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 61-69.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yuyu Chen & Ruodu Wang, 2024. "Infinite-mean models in risk management: Discussions and recent advances," Papers 2408.08678, arXiv.org, revised Oct 2024.
    2. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.
    3. Furrer, Hansjorg & Michna, Zbigniew & Weron, Aleksander, 1997. "Stable Lévy motion approximation in collective risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 20(2), pages 97-114, September.
    4. Dassios, Angelos & Qu, Yan & Zhao, Hongbiao, 2018. "Exact simulation for a class of tempered stable," LSE Research Online Documents on Economics 86981, London School of Economics and Political Science, LSE Library.
    5. J.-F. Chamayou, 2001. "Pseudo random numbers for the Landau and Vavilov distributions," Computational Statistics, Springer, vol. 16(1), pages 131-152, March.
    6. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    7. Luc Devroye & Lancelot James, 2014. "On simulation and properties of the stable law," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 307-343, August.
    8. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    9. John C. Frain, 2007. "Small sample power of tests of normality when the alternative is an alpha-stable distribution," Trinity Economics Papers tep0207, Trinity College Dublin, Department of Economics.
    10. Harry Pavlopoulos & George Chronis, 2023. "On highly skewed fractional log‐stable noise sequences and their application," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(4), pages 337-358, July.
    11. Chronis, George A., 2016. "Modelling the extreme variability of the US Consumer Price Index inflation with a stable non-symmetric distribution," Economic Modelling, Elsevier, vol. 59(C), pages 271-277.
    12. Taufer, Emanuele, 2015. "On the empirical process of strongly dependent stable random variables: asymptotic properties, simulation and applications," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 262-271.
    13. Goddard, John & Onali, Enrico, 2012. "Self-affinity in financial asset returns," International Review of Financial Analysis, Elsevier, vol. 24(C), pages 1-11.
    14. Guarcello, C., 2021. "Lévy noise effects on Josephson junctions," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    15. Mbakob Yonkeu, R. & David, Afungchui, 2022. "Coherence and stochastic resonance in the fractional-birhythmic self-sustained system subjected to fractional time-delay feedback and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    16. Guo, Yongfeng & Wang, Linjie & Wei, Fang & Tan, Jianguo, 2019. "Dynamical behavior of simplified FitzHugh-Nagumo neural system driven by Lévy noise and Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 118-126.
    17. Kotchoni, Rachidi, 2012. "Applications of the characteristic function-based continuum GMM in finance," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3599-3622.
    18. Borak, Szymon & Misiorek, Adam & Weron, Rafał, 2010. "Models for heavy-tailed asset returns," SFB 649 Discussion Papers 2010-049, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    19. Danish A. Ahmed & Sergei V. Petrovskii & Paulo F. C. Tilles, 2018. "The “Lévy or Diffusion” Controversy: How Important Is the Movement Pattern in the Context of Trapping?," Mathematics, MDPI, vol. 6(5), pages 1-27, May.
    20. Szczurek, Andrzej & Maciejewska, Monika & Wyłomańska, Agnieszka & Sikora, Grzegorz & Balcerek, Michał & Teuerle, Marek, 2016. "Discrimination of particulate matter emission sources using stochastic methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 452-466.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2505.01739. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.