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Technical Note—An Unexpected Stochastic Dominance: Pareto Distributions, Dependence, and Diversification

Author

Listed:
  • Yuyu Chen

    (Department of Economics, University of Melbourne, Melbourne, Victoria 3010, Australia)

  • Paul Embrechts

    (RiskLab, Department of Mathematics and ETH Risk Center, ETH Zurich, 8092 Zurich, Switzerland)

  • Ruodu Wang

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

Abstract

We find the perhaps surprising inequality that the weighted average of independent and identically distributed Pareto random variables with infinite mean is larger than one such random variable in the sense of first-order stochastic dominance. This result holds for more general models including super-Pareto distributions, negative dependence, and triggering events and yields superadditivity of the risk measure value-at-risk for these models.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:73:y:2025:i:3:p:1336-1344
    DOI: 10.1287/opre.2022.0505
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