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Diversification for infinite-mean Pareto models without risk aversion

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  • Chen, Yuyu
  • Hu, Taizhong
  • Wang, Ruodu
  • Zou, Zhenfeng

Abstract

We study stochastic dominance between portfolios of independent and identically distributed (iid) extremely heavy-tailed (i.e., infinite-mean) Pareto random variables. With the notion of majorization order, we show that a more diversified portfolio of iid extremely heavy-tailed Pareto random variables is larger in the sense of first-order stochastic dominance. This result is further generalized for Pareto random variables caused by triggering events, random variables with tails being Pareto, bounded Pareto random variables, and positively dependent Pareto random variables. These results provide an important implication in investment: Diversification of extremely heavy-tailed Pareto profits uniformly increases investors’ profitability, leading to a diversification benefit. Remarkably, different from the finite-mean setting, such a diversification benefit does not depend on the decision maker’s risk aversion.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:323:y:2025:i:1:p:341-350
    DOI: 10.1016/j.ejor.2025.01.039
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    References listed on IDEAS

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    1. Rustam Ibragimov, 2009. "Portfolio diversification and value at risk under thick-tailedness," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 565-580.
    2. Silverberg, Gerald & Verspagen, Bart, 2007. "The size distribution of innovations revisited: An application of extreme value statistics to citation and value measures of patent significance," Journal of Econometrics, Elsevier, vol. 139(2), pages 318-339, August.
    3. Pierpaolo Andriani & Bill McKelvey, 2007. "Beyond Gaussian averages: redirecting international business and management research toward extreme events and power laws," Journal of International Business Studies, Palgrave Macmillan;Academy of International Business, vol. 38(7), pages 1212-1230, December.
    4. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
    5. Mincheol Choi & Chang-Yang Lee, 2020. "Power-law distributions of corporate innovative output: evidence from U.S. patent data," Scientometrics, Springer;Akadémiai Kiadó, vol. 122(1), pages 519-554, January.
    6. Yuyu Chen & Paul Embrechts & Ruodu Wang, 2022. "An unexpected stochastic dominance: Pareto distributions, dependence, and diversification," Papers 2208.08471, arXiv.org, revised Mar 2024.
    7. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    8. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    9. Yuyu Chen & Paul Embrechts & Ruodu Wang, 2024. "Risk exchange under infinite-mean Pareto models," Papers 2403.20171, arXiv.org, revised Jun 2025.
    10. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    11. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    12. Sarabia, José María & Gómez-Déniz, Emilio & Prieto, Faustino & Jordá, Vanesa, 2016. "Risk aggregation in multivariate dependent Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 154-163.
    13. Samuelson, Paul A., 1967. "General Proof that Diversification Pays*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(1), pages 1-13, March.
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    Cited by:

    1. Yuyu Chen & Taizhong Hu & Seva Shneer & Zhenfeng Zou, 2025. "Stochastic dominance for linear combinations of infinite-mean risks," Papers 2505.01739, arXiv.org.

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